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class="vector-toc-link" href="#Definitions"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Definitions</span> </div> </a> <ul id="toc-Definitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Basics_of_a_reliability_assessment" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Basics_of_a_reliability_assessment"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Basics of a reliability assessment</span> </div> </a> <ul id="toc-Basics_of_a_reliability_assessment-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Reliability_and_availability_program_plan" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_and_availability_program_plan"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Reliability and availability program plan</span> </div> </a> <ul id="toc-Reliability_and_availability_program_plan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reliability_requirements" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_requirements"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Reliability requirements</span> </div> </a> <ul id="toc-Reliability_requirements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reliability_culture_/_human_errors_/_human_factors" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_culture_/_human_errors_/_human_factors"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Reliability culture / human errors / human factors</span> </div> </a> <ul id="toc-Reliability_culture_/_human_errors_/_human_factors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reliability_prediction_and_improvement" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_prediction_and_improvement"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Reliability prediction and improvement</span> </div> </a> <button aria-controls="toc-Reliability_prediction_and_improvement-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Reliability prediction and improvement subsection</span> </button> <ul id="toc-Reliability_prediction_and_improvement-sublist" class="vector-toc-list"> <li id="toc-Design_for_reliability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Design_for_reliability"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Design for reliability</span> </div> </a> <ul id="toc-Design_for_reliability-sublist" class="vector-toc-list"> <li id="toc-Statistics-based_approach_(i.e._MTBF)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Statistics-based_approach_(i.e._MTBF)"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.1</span> <span>Statistics-based approach (i.e. MTBF)</span> </div> </a> <ul id="toc-Statistics-based_approach_(i.e._MTBF)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physics-of-failure-based_approach" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Physics-of-failure-based_approach"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.2</span> <span>Physics-of-failure-based approach</span> </div> </a> <ul id="toc-Physics-of-failure-based_approach-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Common_tools_and_techniques" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Common_tools_and_techniques"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1.3</span> <span>Common tools and techniques</span> </div> </a> <ul id="toc-Common_tools_and_techniques-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-The_importance_of_language" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_importance_of_language"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>The importance of language</span> </div> </a> <ul id="toc-The_importance_of_language-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Reliability_modeling" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_modeling"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Reliability modeling</span> </div> </a> <button aria-controls="toc-Reliability_modeling-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Reliability modeling subsection</span> </button> <ul id="toc-Reliability_modeling-sublist" class="vector-toc-list"> <li id="toc-Reliability_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reliability_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Reliability theory</span> </div> </a> <ul id="toc-Reliability_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantitative_system_reliability_parameters—theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantitative_system_reliability_parameters—theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Quantitative system reliability parameters—theory</span> </div> </a> <ul id="toc-Quantitative_system_reliability_parameters—theory-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Reliability_testing" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_testing"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Reliability testing</span> </div> </a> <button aria-controls="toc-Reliability_testing-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Reliability testing subsection</span> </button> <ul id="toc-Reliability_testing-sublist" class="vector-toc-list"> <li id="toc-Reliability_test_requirements" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reliability_test_requirements"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Reliability test requirements</span> </div> </a> <ul id="toc-Reliability_test_requirements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Testing_method" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Testing_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Testing method</span> </div> </a> <ul id="toc-Testing_method-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Accelerated_testing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Accelerated_testing"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Accelerated testing</span> </div> </a> <ul id="toc-Accelerated_testing-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Software_reliability" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Software_reliability"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Software reliability</span> </div> </a> <ul id="toc-Software_reliability-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Structural_reliability" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Structural_reliability"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Structural reliability</span> </div> </a> <ul id="toc-Structural_reliability-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Comparison_to_safety_engineering" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Comparison_to_safety_engineering"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Comparison to safety engineering</span> </div> </a> <button aria-controls="toc-Comparison_to_safety_engineering-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Comparison to safety engineering subsection</span> </button> <ul id="toc-Comparison_to_safety_engineering-sublist" class="vector-toc-list"> <li id="toc-Fault_tolerance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fault_tolerance"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.1</span> <span>Fault tolerance</span> </div> </a> <ul id="toc-Fault_tolerance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Basic_reliability_and_mission_reliability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Basic_reliability_and_mission_reliability"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.2</span> <span>Basic reliability and mission reliability</span> </div> </a> <ul id="toc-Basic_reliability_and_mission_reliability-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Detectability_and_common_cause_failures" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Detectability_and_common_cause_failures"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.3</span> <span>Detectability and common cause failures</span> </div> </a> <ul id="toc-Detectability_and_common_cause_failures-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Reliability_versus_quality_(Six_Sigma)" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_versus_quality_(Six_Sigma)"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Reliability versus quality (Six Sigma)</span> </div> </a> <ul id="toc-Reliability_versus_quality_(Six_Sigma)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reliability_operational_assessment" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_operational_assessment"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Reliability operational assessment</span> </div> </a> <ul id="toc-Reliability_operational_assessment-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reliability_organizations" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Reliability_organizations"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Reliability organizations</span> </div> </a> <ul id="toc-Reliability_organizations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Education" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Education"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>Education</span> </div> </a> <ul id="toc-Education-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">16</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">17</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">18</span> <span>Further reading</span> </div> </a> <button aria-controls="toc-Further_reading-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Further reading subsection</span> </button> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> <li id="toc-US_standards,_specifications,_and_handbooks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#US_standards,_specifications,_and_handbooks"> <div class="vector-toc-text"> <span class="vector-toc-numb">18.1</span> <span>US standards, specifications, and handbooks</span> </div> </a> <ul id="toc-US_standards,_specifications,_and_handbooks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-UK_standards" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#UK_standards"> <div class="vector-toc-text"> <span class="vector-toc-numb">18.2</span> <span>UK standards</span> </div> </a> <ul id="toc-UK_standards-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-French_standards" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#French_standards"> <div class="vector-toc-text"> <span class="vector-toc-numb">18.3</span> <span>French standards</span> </div> </a> <ul id="toc-French_standards-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-International_standards" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#International_standards"> <div class="vector-toc-text"> <span class="vector-toc-numb">18.4</span> <span>International standards</span> </div> </a> <ul id="toc-International_standards-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">19</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Reliability engineering: Difference between revisions</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 20 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-20" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">20 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%B3%D8%A9_%D8%A7%D9%84%D9%88%D8%AB%D9%88%D9%82%D9%8A%D8%A9" title="هندسة الوثوقية – Arabic" lang="ar" hreflang="ar" data-title="هندسة الوثوقية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Enginyeria_de_fiabilitat" title="Enginyeria de fiabilitat – Catalan" lang="ca" hreflang="ca" data-title="Enginyeria de fiabilitat" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Spolehlivostn%C3%AD_in%C5%BEen%C3%BDrstv%C3%AD" title="Spolehlivostní inženýrství – Czech" lang="cs" hreflang="cs" data-title="Spolehlivostní inženýrství" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Betriebssicherheit" title="Betriebssicherheit – German" lang="de" hreflang="de" data-title="Betriebssicherheit" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ingenier%C3%ADa_de_confiabilidad" title="Ingeniería de confiabilidad – Spanish" lang="es" hreflang="es" data-title="Ingeniería de confiabilidad" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Fidagarritasun_(ingeniaritza)" title="Fidagarritasun (ingeniaritza) – Basque" lang="eu" hreflang="eu" data-title="Fidagarritasun (ingeniaritza)" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%87%D9%86%D8%AF%D8%B3%DB%8C_%D9%82%D8%A7%D8%A8%D9%84%DB%8C%D8%AA_%D8%A7%D8%B7%D9%85%DB%8C%D9%86%D8%A7%D9%86" title="مهندسی قابلیت اطمینان – Persian" lang="fa" hreflang="fa" data-title="مهندسی قابلیت اطمینان" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ing%C3%A9nierie_de_fiabilit%C3%A9" title="Ingénierie de fiabilité – French" lang="fr" hreflang="fr" data-title="Ingénierie de fiabilité" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8B%A0%EB%A2%B0%EC%84%B1_%EA%B3%B5%ED%95%99" title="신뢰성 공학 – Korean" lang="ko" hreflang="ko" data-title="신뢰성 공학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B6%E0%A5%8D%E0%A4%B5%E0%A4%B8%E0%A4%A8%E0%A5%80%E0%A4%AF%E0%A4%A4%E0%A4%BE_%E0%A4%87%E0%A4%82%E0%A4%9C%E0%A5%80%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%B0%E0%A5%80" title="विश्वसनीयता इंजीनियरी – Hindi" lang="hi" hreflang="hi" data-title="विश्वसनीयता इंजीनियरी" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/In%C5%BEenjerstvo_pouzdanosti" title="Inženjerstvo pouzdanosti – Croatian" lang="hr" hreflang="hr" data-title="Inženjerstvo pouzdanosti" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ingegneria_dell%27affidabilit%C3%A0" title="Ingegneria dell'affidabilità – Italian" lang="it" hreflang="it" data-title="Ingegneria dell'affidabilità" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Megb%C3%ADzhat%C3%B3s%C3%A1gi_tervez%C3%A9s" title="Megbízhatósági tervezés – Hungarian" lang="hu" hreflang="hu" data-title="Megbízhatósági tervezés" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Reliability_engineering" title="Reliability engineering – Dutch" lang="nl" hreflang="nl" data-title="Reliability engineering" data-language-autonym="Nederlands" 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The reliability of the product in all environments such as expected use, transportation, or storage during the specified lifespan should be considered.<ref name="sciencedirect.com"/> It is to expose the product to natural or artificial environmental conditions to undergo its action to evaluate the performance of the product<del class="diffchange diffchange-inline"> [[https://relteck.com/reliability-testing/|Reliablity testing]] </del> under the environmental conditions of actual use, transportation, and storage, and to analyze and study the degree of influence of environmental factors and their mechanism of action.<ref>{{Cite book|last1=Zhang|first1=J.|last2=Geiger|first2=C.|last3=Sun|first3=F.|title=2016 Annual Reliability and Maintainability Symposium (RAMS) |chapter=A system approach to reliability verification test design |date=January 2016|chapter-url=https://ieeexplore.ieee.org/document/7448014|pages=1–6|doi=10.1109/RAMS.2016.7448014|isbn=978-1-5090-0249-8|s2cid=24770411}}</ref> Through the use of various environmental test equipment to simulate the high temperature, low temperature, and high humidity, and temperature changes in the climate environment, to accelerate the reaction of the product in the use environment, to verify whether it reaches the expected quality in [[R&D]], design, and manufacturing.<ref>{{Cite journal|last1=Dai|first1=Wei|last2=Maropoulos|first2=Paul G.|last3=Zhao|first3=Yu|date=2015-01-02|title=Reliability modelling and verification of manufacturing processes based on process knowledge management|url=https://doi.org/10.1080/0951192X.2013.834462|journal=International Journal of Computer Integrated Manufacturing|volume=28|issue=1|pages=98–111|doi=10.1080/0951192X.2013.834462|s2cid=32995968|issn=0951-192X}}</ref></div></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div>The purpose of '''reliability testing''' or '''reliability verification''' is to discover potential problems with the design as early as possible and, ultimately, provide confidence that the system meets its reliability requirements. The reliability of the product in all environments such as expected use, transportation, or storage during the specified lifespan should be considered.<ref name="sciencedirect.com"/> It is to expose the product to natural or artificial environmental conditions to undergo its action to evaluate the performance of the product under the environmental conditions of actual use, transportation, and storage, and to analyze and study the degree of influence of environmental factors and their mechanism of action.<ref>{{Cite book|last1=Zhang|first1=J.|last2=Geiger|first2=C.|last3=Sun|first3=F.|title=2016 Annual Reliability and Maintainability Symposium (RAMS) |chapter=A system approach to reliability verification test design |date=January 2016|chapter-url=https://ieeexplore.ieee.org/document/7448014|pages=1–6|doi=10.1109/RAMS.2016.7448014|isbn=978-1-5090-0249-8|s2cid=24770411}}</ref> Through the use of various environmental test equipment to simulate the high temperature, low temperature, and high humidity, and temperature changes in the climate environment, to accelerate the reaction of the product in the use environment, to verify whether it reaches the expected quality in [[R&D]], design, and manufacturing.<ref>{{Cite journal|last1=Dai|first1=Wei|last2=Maropoulos|first2=Paul G.|last3=Zhao|first3=Yu|date=2015-01-02|title=Reliability modelling and verification of manufacturing processes based on process knowledge management|url=https://doi.org/10.1080/0951192X.2013.834462|journal=International Journal of Computer Integrated Manufacturing|volume=28|issue=1|pages=98–111|doi=10.1080/0951192X.2013.834462|s2cid=32995968|issn=0951-192X}}</ref></div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>Reliability verification is also called reliability testing, which refers to the use of modeling, statistics, and other methods to evaluate the reliability of the product based on the product's life span and expected performance.<ref>{{Cite web|title=Reliability Verification for AI and ML Processors - White Paper|url=https://www.allaboutcircuits.com/industry-white-papers/reliability-verification-for-ai-and-ml-processors/|access-date=2020-12-11|website=www.allaboutcircuits.com|language=en}}</ref> Most product on the market requires reliability testing, such as automotive, [[integrated circuit]], heavy machinery used to mine nature resources, Aircraft auto software.<ref>{{Cite journal|last1=Weber|first1=Wolfgang|last2=Tondok|first2=Heidemarie|last3=Bachmayer|first3=Michael|date=2005-07-01|title=Enhancing software safety by fault trees: experiences from an application to flight critical software|url=http://www.sciencedirect.com/science/article/pii/S0951832004001760|journal=Reliability Engineering & System Safety|series=Safety, Reliability and Security of Industrial Computer Systems|language=en|volume=89|issue=1|pages=57–70|doi=10.1016/j.ress.2004.08.007|issn=0951-8320}}</ref><ref>{{Cite journal|last1=Ren|first1=Yuanqiang|last2=Tao|first2=Jingya|last3=Xue|first3=Zhaopeng|date=January 2020|title=Design of a Large-Scale Piezoelectric Transducer Network Layer and Its Reliability Verification for Space Structures|journal=Sensors|language=en|volume=20|issue=15|pages=4344|doi=10.3390/s20154344|pmid=32759794|pmc=7435873|bibcode=2020Senso..20.4344R|doi-access=free}}</ref></div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>Reliability verification is also called reliability testing, which refers to the use of modeling, statistics, and other methods to evaluate the reliability of the product based on the product's life span and expected performance.<ref>{{Cite web|title=Reliability Verification for AI and ML Processors - White Paper|url=https://www.allaboutcircuits.com/industry-white-papers/reliability-verification-for-ai-and-ml-processors/|access-date=2020-12-11|website=www.allaboutcircuits.com|language=en}}</ref> Most product on the market requires reliability testing, such as automotive, [[integrated circuit]], heavy machinery used to mine nature resources, Aircraft auto software.<ref>{{Cite journal|last1=Weber|first1=Wolfgang|last2=Tondok|first2=Heidemarie|last3=Bachmayer|first3=Michael|date=2005-07-01|title=Enhancing software safety by fault trees: experiences from an application to flight critical software|url=http://www.sciencedirect.com/science/article/pii/S0951832004001760|journal=Reliability Engineering & System Safety|series=Safety, Reliability and Security of Industrial Computer Systems|language=en|volume=89|issue=1|pages=57–70|doi=10.1016/j.ress.2004.08.007|issn=0951-8320}}</ref><ref>{{Cite journal|last1=Ren|first1=Yuanqiang|last2=Tao|first2=Jingya|last3=Xue|first3=Zhaopeng|date=January 2020|title=Design of a Large-Scale Piezoelectric Transducer Network Layer and Its Reliability Verification for Space Structures|journal=Sensors|language=en|volume=20|issue=15|pages=4344|doi=10.3390/s20154344|pmid=32759794|pmc=7435873|bibcode=2020Senso..20.4344R|doi-access=free}}</ref></div></td> </tr> </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>Revision as of 00:35, 23 November 2024</h2> <div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Sub-discipline of systems engineering that emphasizes dependability</div> <p class="mw-empty-elt"> </p><p><b>Reliability engineering</b> is a sub-discipline of <a href="/wiki/Systems_engineering" title="Systems engineering">systems engineering</a> that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, OR will operate in a defined environment without failure.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Reliability is closely related to <a href="/wiki/Availability" title="Availability">availability</a>, which is typically described as the ability of a component or system to function at a specified moment or interval of time. </p><p>The <i>reliability function</i> is theoretically defined as the <a href="/wiki/Probability" title="Probability">probability</a> of success. In practice, it is calculated using different techniques, and its value ranges between 0 and 1, where 0 indicates no probability of success while 1 indicates definite success. This probability is estimated from detailed (physics of failure) analysis, previous data sets, or through reliability testing and reliability modeling. <a href="/wiki/Availability" title="Availability">Availability</a>, <a href="/wiki/Testability" title="Testability">testability</a>, <a href="/wiki/Maintainability" title="Maintainability">maintainability</a>, and <a href="/wiki/Maintenance,_repair_and_operations" class="mw-redirect" title="Maintenance, repair and operations">maintenance</a> are often defined as a part of "reliability engineering" in reliability programs. Reliability often plays a key role in the <a href="/wiki/Cost-effectiveness" class="mw-redirect" title="Cost-effectiveness">cost-effectiveness</a> of systems. </p><p>Reliability engineering deals with the prediction, prevention, and management of high levels of "<a href="/wiki/Service_life" title="Service life">lifetime</a>" engineering <a href="/wiki/Uncertainty" title="Uncertainty">uncertainty</a> and <a href="/wiki/Risk" title="Risk">risks</a> of failure. Although <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> parameters define and affect reliability, reliability is not only achieved by mathematics and statistics.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> "Nearly all teaching and literature on the subject emphasize these aspects and ignore the reality that the ranges of uncertainty involved largely invalidate quantitative methods for <a href="/wiki/Prediction" title="Prediction">prediction</a> and measurement."<sup id="cite_ref-O'Connor_2002_4-0" class="reference"><a href="#cite_note-O'Connor_2002-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> For example, it is easy to represent "probability of failure" as a symbol or value in an equation, but it is almost impossible to predict its true magnitude in practice, which is massively <a href="/wiki/Multivariate_statistics" title="Multivariate statistics">multivariate</a>, so having the equation for reliability does not begin to equal having an accurate predictive measurement of reliability. </p><p>Reliability engineering relates closely to Quality Engineering, <a href="/wiki/Safety_engineering" title="Safety engineering">safety engineering</a>, and <a href="/wiki/System_safety" title="System safety">system safety</a>, in that they use common methods for their analysis and may require input from each other. It can be said that a system must be reliably safe. </p><p>Reliability engineering focuses on the costs of failure caused by system downtime, cost of spares, repair equipment, personnel, and cost of warranty claims.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2></div> <p>The word <i>reliability</i> can be traced back to 1816 and is first attested to the poet <a href="/wiki/Samuel_Taylor_Coleridge" title="Samuel Taylor Coleridge">Samuel Taylor Coleridge</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Before World War II the term was linked mostly to <a href="/wiki/Repeatability" title="Repeatability">repeatability</a>; a test (in any type of science) was considered "reliable" if the same results would be obtained repeatedly. In the 1920s, product improvement through the use of <a href="/wiki/Statistical_process_control" title="Statistical process control">statistical process control</a> was promoted by Dr. <a href="/wiki/Walter_A._Shewhart" title="Walter A. Shewhart">Walter A. Shewhart</a> at <a href="/wiki/Bell_Labs" title="Bell Labs">Bell Labs</a>,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> around the time that <a href="/wiki/Waloddi_Weibull" title="Waloddi Weibull">Waloddi Weibull</a> was working on statistical models for fatigue. The development of reliability engineering was here on a parallel path with quality. The modern use of the word reliability was defined by the U.S. military in the 1940s, characterizing a product that would operate when expected and for a specified period. </p><p>In World War II, many reliability issues were due to the inherent unreliability of electronic equipment available at the time, and to fatigue issues. In 1945, M.A. Miner published a seminal paper titled "Cumulative Damage in Fatigue" in an ASME journal. A main application for reliability engineering in the military was for the vacuum tube as used in radar systems and other electronics, for which reliability proved to be very problematic and costly. The <a href="/wiki/Institute_of_Electrical_and_Electronics_Engineers" title="Institute of Electrical and Electronics Engineers">IEEE</a> formed the Reliability Society in 1948. In 1950, the <a href="/wiki/United_States_Department_of_Defense" title="United States Department of Defense">United States Department of Defense</a> formed a group called the "Advisory Group on the Reliability of Electronic Equipment" (AGREE) to investigate reliability methods for military equipment.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> This group recommended three main ways of working: </p> <ul><li>Improve component reliability.</li> <li>Establish quality and reliability requirements for suppliers.</li> <li>Collect field data and find root causes of failures.</li></ul> <p>In the 1960s, more emphasis was given to reliability testing on component and system levels. The famous military standard MIL-STD-781 was created at that time. Around this period also the much-used predecessor to military handbook 217 was published by <a href="/wiki/RCA" title="RCA">RCA</a> and was used for the prediction of failure rates of electronic components. The emphasis on component reliability and empirical research (e.g. Mil Std 217) alone slowly decreased. More pragmatic approaches, as used in the consumer industries, were being used. In the 1980s, televisions were increasingly made up of solid-state semiconductors. Automobiles rapidly increased their use of semiconductors with a variety of microcomputers under the hood and in the dash. Large air conditioning systems developed electronic controllers, as did microwave ovens and a variety of other appliances. Communications systems began to adopt electronics to replace older mechanical switching systems. <a href="/wiki/Telcordia_Technologies" class="mw-redirect" title="Telcordia Technologies">Bellcore</a> issued the first consumer prediction methodology for telecommunications, and <a href="/wiki/SAE_International" title="SAE International">SAE</a> developed a similar document SAE870050 for automotive applications. The nature of predictions evolved during the decade, and it became apparent that die complexity wasn't the only factor that determined failure rates for integrated circuits (ICs). Kam Wong published a paper questioning the bathtub curve<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>—see also <a href="/wiki/Reliability-centered_maintenance" title="Reliability-centered maintenance">reliability-centered maintenance</a>. During this decade, the failure rate of many components dropped by a factor of 10. Software became important to the reliability of systems. By the 1990s, the pace of IC development was picking up. Wider use of stand-alone microcomputers was common, and the PC market helped keep IC densities following Moore's law and doubling about every 18 months. Reliability engineering was now changing as it moved towards understanding the <a href="/wiki/Physics_of_failure" title="Physics of failure">physics of failure</a>. Failure rates for components kept dropping, but system-level issues became more prominent. <a href="/wiki/Systems_thinking" title="Systems thinking">Systems thinking</a> has become more and more important. For software, the CMM model (<a href="/wiki/Capability_Maturity_Model" title="Capability Maturity Model">Capability Maturity Model</a>) was developed, which gave a more qualitative approach to reliability. ISO 9000 added reliability measures as part of the design and development portion of certification. The expansion of the World Wide Web created new challenges of security and trust. The older problem of too little reliable information available had now been replaced by too much information of questionable value. Consumer reliability problems could now be discussed online in real-time using data. New technologies such as micro-electromechanical systems (<a href="/wiki/Microelectromechanical_systems" class="mw-redirect" title="Microelectromechanical systems">MEMS</a>), handheld <a href="/wiki/Global_Positioning_System" title="Global Positioning System">GPS</a>, and hand-held devices that combine cell phones and computers all represent challenges to maintaining reliability. Product development time continued to shorten through this decade and what had been done in three years was being done in 18 months. This meant that reliability tools and tasks had to be more closely tied to the development process itself. In many ways, reliability has become part of everyday life and consumer expectations. </p> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2></div> <p>Reliability is the probability of a product performing its intended function under specified operating conditions in a manner that meets or exceeds customer expectations.<sup id="cite_ref-sciencedirect.com_10-0" class="reference"><a href="#cite_note-sciencedirect.com-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Objective">Objective</h3></div> <p>The objectives of reliability engineering, in decreasing order of priority, are:<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <ol><li>To apply engineering knowledge and specialist techniques to prevent or to reduce the likelihood or frequency of failures.</li> <li>To identify and correct the causes of failures that do occur despite the efforts to prevent them.</li> <li>To determine ways of coping with failures that do occur, if their causes have not been corrected.</li> <li>To apply methods for estimating the likely reliability of new designs, and for analysing reliability data.</li></ol> <p>The reason for the priority emphasis is that it is by far the most effective way of working, in terms of minimizing costs and generating reliable products. The primary skills that are required, therefore, are the ability to understand and anticipate the possible causes of failures, and knowledge of how to prevent them. It is also necessary to know the methods that can be used for analyzing designs and data. </p> <div class="mw-heading mw-heading3"><h3 id="Scope_and_techniques">Scope and techniques</h3></div> <p>Reliability engineering for "<a href="/wiki/Complex_systems" class="mw-redirect" title="Complex systems">complex systems</a>" requires a different, more elaborate systems approach than for non-complex systems. Reliability engineering may in that case involve: </p> <ul><li>System availability and mission readiness analysis and related reliability and maintenance requirement allocation</li> <li>Functional system failure analysis and derived requirements specification</li> <li>Inherent (system) design reliability analysis and derived requirements specification for both hardware and software design</li> <li>System diagnostics design</li> <li><a href="/wiki/Fault_tolerant_system" class="mw-redirect" title="Fault tolerant system">Fault tolerant systems</a> (e.g. by redundancy)</li> <li>Predictive and <a href="/wiki/Preventive_maintenance" class="mw-redirect" title="Preventive maintenance">preventive maintenance</a> (e.g. reliability-centered maintenance)</li> <li>Human factors / human interaction / human errors</li> <li>Manufacturing- and assembly-induced failures (effect on the detected "0-hour quality" and reliability)</li> <li>Maintenance-induced failures</li> <li>Transport-induced failures</li> <li>Storage-induced failures</li> <li>Use (load) studies, component stress analysis, and derived requirements specification</li> <li>Software (systematic) failures</li> <li>Failure / reliability testing (and derived requirements)</li> <li>Field failure monitoring and corrective actions</li> <li><a href="/wiki/Spare_part" title="Spare part">Spare parts</a> stocking (availability control)</li> <li>Technical documentation, caution and warning analysis</li> <li>Data and information acquisition/organisation (creation of a general reliability development hazard log and <a href="/wiki/Failure_reporting,_analysis,_and_corrective_action_system" title="Failure reporting, analysis, and corrective action system">FRACAS</a> system)</li> <li><a href="/wiki/Chaos_engineering" title="Chaos engineering">Chaos engineering</a></li></ul> <p>Effective reliability engineering requires understanding of the basics of <a href="/wiki/Failure_cause" title="Failure cause">failure mechanisms</a> for which experience, broad engineering skills and good knowledge from many different special fields of engineering are required,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> for example: </p> <ul><li><a href="/wiki/Tribology" title="Tribology">Tribology</a></li> <li><a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress (mechanics)</a></li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a> / <a href="/wiki/Fatigue_(material)" title="Fatigue (material)">fatigue</a></li> <li><a href="/wiki/Thermal_engineering" title="Thermal engineering">Thermal engineering</a></li> <li><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a> / shock-loading engineering</li> <li><a href="/wiki/Electrical_engineering" title="Electrical engineering">Electrical engineering</a></li> <li><a href="/wiki/Chemical_engineering" title="Chemical engineering">Chemical engineering</a> (e.g. <a href="/wiki/Corrosion" title="Corrosion">corrosion</a>)</li> <li><a href="/wiki/Material_science" class="mw-redirect" title="Material science">Material science</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Definitions">Definitions</h3></div> <p>Reliability may be defined in the following ways: </p> <ul><li>The idea that an item is fit for a purpose</li> <li>The capacity of a designed, produced, or maintained item to perform as required</li> <li>The capacity of a population of designed, produced or maintained items to perform as required</li> <li>The resistance to failure of an item</li> <li>The probability of an item to perform a required function under stated conditions</li> <li>The durability of an object</li></ul> <div class="mw-heading mw-heading3"><h3 id="Basics_of_a_reliability_assessment">Basics of a reliability assessment</h3></div> <p>Many engineering techniques are used in reliability <a href="/wiki/Risk_assessment" title="Risk assessment">risk assessments</a>, such as reliability block diagrams, <a href="/wiki/Hazard_analysis" title="Hazard analysis">hazard analysis</a>, <a href="/wiki/Failure_mode_and_effects_analysis" title="Failure mode and effects analysis">failure mode and effects analysis</a> (FMEA),<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Fault_tree_analysis" title="Fault tree analysis">fault tree analysis</a> (FTA), <a href="/wiki/Reliability_Centered_Maintenance" class="mw-redirect" title="Reliability Centered Maintenance">Reliability Centered Maintenance</a>, (probabilistic) load and material stress and wear calculations, (probabilistic) fatigue and creep analysis, human error analysis, manufacturing defect analysis, reliability testing, etc. These analyses must be done properly and with much attention to detail to be effective. Because of the large number of reliability techniques, their expense, and the varying degrees of reliability required for different situations, most projects develop a reliability program plan to specify the reliability tasks (<a href="/wiki/Statement_of_work" title="Statement of work">statement of work</a> (SoW) requirements) that will be performed for that specific system. </p><p>Consistent with the creation of <a href="/wiki/Safety_case" title="Safety case">safety cases</a>, for example per <a href="/wiki/ARP4761" title="ARP4761">ARP4761</a>, the goal of reliability assessments is to provide a robust set of qualitative and quantitative evidence that the use of a component or system will not be associated with unacceptable risk. The basic steps to take<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> are to: </p> <ul><li>Thoroughly identify relevant unreliability "hazards", e.g. potential conditions, events, human errors, failure modes, interactions, failure mechanisms, and root causes, by specific analysis or tests.</li> <li>Assess the associated system risk, by specific analysis or testing.</li> <li>Propose mitigation, e.g. <a href="/wiki/Requirement" title="Requirement">requirements</a>, design changes, detection logic, maintenance, and training, by which the risks may be lowered and controlled at an acceptable level.</li> <li>Determine the best mitigation and get agreement on final, acceptable risk levels, possibly based on cost/benefit analysis.</li></ul> <p>The <a href="/wiki/Risk" title="Risk">risk</a> here is the combination of probability and severity of the failure incident (scenario) occurring. The severity can be looked at from a system safety or a system availability point of view. Reliability for safety can be thought of as a very different focus from reliability for system availability. Availability and safety can exist in dynamic tension as keeping a system too available can be unsafe. Forcing an engineering system into a safe state too quickly can force false alarms that impede the availability of the system. </p><p>In a <i>de minimis</i> definition, the severity of failures includes the cost of spare parts, man-hours, logistics, damage (secondary failures), and downtime of machines which may cause production loss. A more complete definition of failure also can mean injury, dismemberment, and death of people within the system (witness mine accidents, industrial accidents, space shuttle failures) and the same to innocent bystanders (witness the citizenry of cities like Bhopal, Love Canal, Chernobyl, or Sendai, and other victims of the 2011 Tōhoku earthquake and tsunami)—in this case, reliability engineering becomes system safety. What is acceptable is determined by the managing authority or customers or the affected communities. Residual risk is the risk that is left over after all reliability activities have finished, and includes the unidentified risk—and is therefore not completely quantifiable. </p><p>The complexity of the technical systems such as improvements of design and materials, planned inspections, fool-proof design, and backup redundancy decreases risk and increases the cost. The risk can be decreased to ALARA (as low as reasonably achievable) or ALAPA (as low as practically achievable) levels. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_and_availability_program_plan">Reliability and availability program plan</h2></div> <p>Implementing a reliability program is not simply a software purchase; it is not just a checklist of items that must be completed that ensure one has reliable products and processes. A reliability program is a complex learning and knowledge-based system unique to one's products and processes. It is supported by leadership, built on the skills that one develops within a team, integrated into business processes, and executed by following proven standard work practices.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>A reliability program plan is used to document exactly what "best practices" (tasks, methods, tools, analysis, and tests) are required for a particular (sub)system, as well as clarify customer requirements for reliability assessment. For large-scale complex systems, the reliability program plan should be a separate <a href="/wiki/Document" title="Document">document</a>. Resource determination for manpower and budgets for testing and other tasks is critical for a successful program. In general, the amount of work required for an effective program for complex systems is large. </p><p>A reliability program plan is essential for achieving high levels of reliability, testability, <a href="/wiki/Maintainability" title="Maintainability">maintainability</a>, and the resulting system <a href="/wiki/Availability" title="Availability">availability</a>, and is developed early during system development and refined over the system's life cycle. It specifies not only what the reliability engineer does, but also the tasks performed by other <a href="/wiki/Stakeholder_(corporate)" title="Stakeholder (corporate)">stakeholders</a>. An effective reliability program plan must be approved by top program management, which is responsible for the allocation of sufficient resources for its implementation. </p><p>A reliability program plan may also be used to evaluate and improve the availability of a system by the strategy of focusing on increasing testability & maintainability and not on reliability. Improving maintainability is generally easier than improving reliability. Maintainability estimates (repair rates) are also generally more accurate. However, because the uncertainties in the reliability estimates are in most cases very large, they are likely to dominate the availability calculation (prediction uncertainty problem), even when maintainability levels are very high. When reliability is not under control, more complicated issues may arise, like manpower (maintainers/customer service capability) shortages, spare part availability, logistic delays, lack of repair facilities, extensive retrofit and complex configuration management costs, and others. The problem of unreliability may be increased also due to the "domino effect" of maintenance-induced failures after repairs. Focusing only on maintainability is therefore not enough. If failures are prevented, none of the other issues are of any importance, and therefore reliability is generally regarded as the most important part of availability. Reliability needs to be evaluated and improved related to both availability and the <a href="/wiki/Total_cost_of_ownership" title="Total cost of ownership">total cost of ownership</a> (TCO) due to the cost of spare parts, maintenance man-hours, transport costs, storage costs, part obsolete risks, etc. But, as GM and Toyota have belatedly discovered, TCO also includes the downstream liability costs when reliability calculations have not sufficiently or accurately addressed customers' bodily risks. Often a trade-off is needed between the two. There might be a maximum ratio between availability and cost of ownership. The testability of a system should also be addressed in the plan, as this is the link between reliability and maintainability. The maintenance strategy can influence the reliability of a system (e.g., by preventive and/or <a href="/wiki/Predictive_maintenance" title="Predictive maintenance">predictive maintenance</a>), although it can never bring it above the inherent reliability. </p><p>The reliability plan should clearly provide a strategy for availability control. Whether only availability or also cost of ownership is more important depends on the use of the system. For example, a system that is a critical link in a production system—e.g., a big oil platform—is normally allowed to have a very high cost of ownership if that cost translates to even a minor increase in availability, as the unavailability of the platform results in a massive loss of revenue which can easily exceed the high cost of ownership. A proper reliability plan should always address RAMT analysis in its total context. RAMT stands for reliability, availability, maintainability/maintenance, and testability in the context of the customer's needs. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_requirements">Reliability requirements</h2></div> <p>For any system, one of the first tasks of reliability engineering is to adequately specify the reliability and maintainability requirements allocated from the overall <a href="/wiki/Availability" title="Availability">availability</a> needs and, more importantly, derived from proper design failure analysis or preliminary prototype test results. Clear requirements (able to be designed to) should constrain the designers from designing particular unreliable items/constructions/interfaces/systems. Setting only availability, reliability, testability, or maintainability targets (e.g., max. failure rates) is not appropriate. This is a broad misunderstanding about Reliability Requirements Engineering. Reliability requirements address the system itself, including test and assessment requirements, and associated tasks and documentation. Reliability requirements are included in the appropriate system or subsystem requirements specifications, test plans, and contract statements. The creation of proper lower-level requirements is critical.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The provision of only quantitative minimum targets (e.g., <a href="/wiki/Mean_Time_Between_Failure" class="mw-redirect" title="Mean Time Between Failure">Mean Time Between Failure</a> (MTBF) values or failure rates) is not sufficient for different reasons. One reason is that a full validation (related to correctness and verifiability in time) of a quantitative reliability allocation (requirement spec) on lower levels for complex systems can (often) not be made as a consequence of (1) the fact that the requirements are probabilistic, (2) the extremely high level of uncertainties involved for showing compliance with all these probabilistic requirements, and because (3) reliability is a function of time, and accurate estimates of a (probabilistic) reliability number per item are available only very late in the project, sometimes even after many years of in-service use. Compare this problem with the continuous (re-)balancing of, for example, lower-level-system mass requirements in the development of an aircraft, which is already often a big undertaking. Notice that in this case, masses do only differ in terms of only some %, are not a function of time, and the data is non-probabilistic and available already in CAD models. In the case of reliability, the levels of unreliability (failure rates) may change with factors of decades (multiples of 10) as a result of very minor deviations in design, process, or anything else.<sup id="cite_ref-ReferenceA_17-0" class="reference"><a href="#cite_note-ReferenceA-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The information is often not available without huge uncertainties within the development phase. This makes this allocation problem almost impossible to do in a useful, practical, valid manner that does not result in massive over- or under-specification. A pragmatic approach is therefore needed—for example: the use of general levels/classes of quantitative requirements depending only on severity of failure effects. Also, the validation of results is a far more subjective task than any other type of requirement. (Quantitative) reliability parameters—in terms of MTBF—are by far the most uncertain design parameters in any design. </p><p>Furthermore, reliability design requirements should drive a (system or part) design to incorporate features that prevent failures from occurring, or limit consequences from failure in the first place. Not only would it aid in some predictions, this effort would keep from distracting the engineering effort into a kind of accounting work. A design requirement should be precise enough so that a designer can "design to" it and can also prove—through analysis or testing—that the requirement has been achieved, and, if possible, within some a stated confidence. Any type of reliability requirement should be detailed and could be derived from failure analysis (Finite-Element Stress and Fatigue analysis, Reliability Hazard Analysis, FTA, FMEA, Human Factor Analysis, Functional Hazard Analysis, etc.) or any type of reliability testing. Also, requirements are needed for verification tests (e.g., required overload stresses) and test time needed. To derive these requirements in an effective manner, a <a href="/wiki/Systems_engineering" title="Systems engineering">systems engineering</a>-based risk assessment and mitigation logic should be used. Robust hazard log systems must be created that contain detailed information on why and how systems could or have failed. Requirements are to be derived and tracked in this way. These practical design requirements shall drive the design and not be used only for verification purposes. These requirements (often design constraints) are in this way derived from failure analysis or preliminary tests. Understanding of this difference compared to only purely quantitative (logistic) requirement specification (e.g., Failure Rate / MTBF target) is paramount in the development of successful (complex) systems.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>The maintainability requirements address the costs of repairs as well as repair time. Testability (not to be confused with test requirements) requirements provide the link between reliability and maintainability and should address detectability of failure modes (on a particular system level), isolation levels, and the creation of diagnostics (procedures). As indicated above, reliability engineers should also address requirements for various reliability tasks and documentation during system development, testing, production, and operation. These requirements are generally specified in the contract statement of work and depend on how much leeway the customer wishes to provide to the contractor. Reliability tasks include various analyses, planning, and failure reporting. Task selection depends on the criticality of the system as well as cost. A safety-critical system may require a formal failure reporting and review process throughout development, whereas a non-critical system may rely on final test reports. The most common reliability program tasks are documented in reliability program standards, such as MIL-STD-785 and IEEE 1332. Failure reporting analysis and corrective action systems are a common approach for product/process reliability monitoring. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_culture_/_human_errors_/_human_factors"><span id="Reliability_culture_.2F_human_errors_.2F_human_factors"></span>Reliability culture / human errors / human factors</h2></div> <p>In practice, most failures can be traced back to some type of <a href="/wiki/Human_error" title="Human error">human error</a>, for example in: </p> <ul><li>Management decisions (e.g. in budgeting, timing, and required tasks)</li> <li>Systems Engineering: Use studies (load cases)</li> <li>Systems Engineering: Requirement analysis / setting</li> <li>Systems Engineering: Configuration control</li> <li>Assumptions</li> <li>Calculations / simulations / FEM analysis</li> <li>Design</li> <li>Design drawings</li> <li>Testing (e.g. incorrect load settings or failure measurement)</li> <li>Statistical analysis</li> <li>Manufacturing</li> <li>Quality control</li> <li>Maintenance</li> <li>Maintenance manuals</li> <li>Training</li> <li>Classifying and ordering of information</li> <li>Feedback of field information (e.g. incorrect or too vague)</li> <li>etc.</li></ul> <p>However, humans are also very good at detecting such failures, correcting them, and improvising when abnormal situations occur. Therefore, policies that completely rule out human actions in design and production processes to improve reliability may not be effective. Some tasks are better performed by humans and some are better performed by machines.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Furthermore, human errors in management; the organization of data and information; or the misuse or abuse of items, may also contribute to unreliability. This is the core reason why high levels of reliability for complex systems can only be achieved by following a robust <a href="/wiki/Systems_engineering" title="Systems engineering">systems engineering</a> process with proper planning and execution of the validation and verification tasks. This also includes the careful organization of data and information sharing and creating a "reliability culture", in the same way, that having a "safety culture" is paramount in the development of safety-critical systems. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_prediction_and_improvement">Reliability prediction and improvement</h2></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Risk_Assessment#Quantitative_risk_assessment" class="mw-redirect" title="Risk Assessment">Risk Assessment § Quantitative risk assessment</a></div> <p>Reliability prediction combines: </p> <ul><li>creation of a proper reliability model (see further on this page)</li> <li>estimation (and justification) of input parameters for this model (e.g. failure rates for a particular failure mode or event and the mean time to repair the system for a particular failure)</li> <li>estimation of output reliability parameters at system or part level (i.e. system availability or frequency of a particular functional failure) The emphasis on quantification and target setting (e.g. MTBF) might imply there is a limit to achievable reliability, however, there is no inherent limit and development of higher reliability does not need to be more costly. In addition, they<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag possibly uses too-vague attribution or weasel words. (December 2023)">who?</span></a></i>]</sup> argue that prediction of reliability from historic data can be very misleading, with comparisons only valid for identical designs, products, manufacturing processes, and maintenance with identical operating loads and usage environments. Even minor changes in any of these could have major effects on reliability. Furthermore, the most unreliable and important items (i.e. the most interesting candidates for a reliability investigation) are most likely to be modified and re-engineered since historical data was gathered, making the standard (re-active or pro-active) statistical methods and processes used in e.g. medical or insurance industries less effective. Another surprising – but logical – argument is that to be able to accurately predict reliability by testing, the exact mechanisms of failure must be known and therefore – in most cases – could be prevented! Following the incorrect route of trying to quantify and solve a complex reliability engineering problem in terms of MTBF or probability using an-incorrect – for example, the re-active – approach is referred to by Barnard as "Playing the Numbers Game" and is regarded as bad practice.<sup id="cite_ref-lambda_20-0" class="reference"><a href="#cite_note-lambda-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li></ul> <p>For existing systems, it is arguable that any attempt by a responsible program to correct the root cause of discovered failures may render the initial MTBF estimate invalid, as new assumptions (themselves subject to high error levels) of the effect of this correction must be made. Another practical issue is the general unavailability of detailed failure data, with those available often featuring inconsistent filtering of failure (feedback) data, and ignoring statistical errors (which are very high for rare events like reliability related failures). Very clear guidelines must be present to count and compare failures related to different type of root-causes (e.g. manufacturing-, maintenance-, transport-, system-induced or inherent design failures). Comparing different types of causes may lead to incorrect estimations and incorrect business decisions about the focus of improvement. </p><p>To perform a proper quantitative reliability prediction for systems may be difficult and very expensive if done by testing. At the individual part-level, reliability results can often be obtained with comparatively high confidence, as testing of many sample parts might be possible using the available testing budget. However, unfortunately these tests may lack validity at a system-level due to assumptions made at part-level testing. These authors emphasized the importance of initial part- or system-level testing until failure, and to learn from such failures to improve the system or part. The general conclusion is drawn that an accurate and absolute prediction – by either field-data comparison or testing – of reliability is in most cases not possible. An exception might be failures due to wear-out problems such as fatigue failures. In the introduction of MIL-STD-785 it is written that reliability prediction should be used with great caution, if not used solely for comparison in trade-off studies. </p> <div class="mw-heading mw-heading3"><h3 id="Design_for_reliability">Design for reliability</h3></div> <p>Design for Reliability (DfR) is a process that encompasses tools and procedures to ensure that a product meets its reliability requirements, under its use environment, for the duration of its lifetime. DfR is implemented in the design stage of a product to proactively improve product reliability.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> DfR is often used as part of an overall <a href="/wiki/Design_for_X" title="Design for X">Design for Excellence (DfX)</a> strategy. </p> <div class="mw-heading mw-heading4"><h4 id="Statistics-based_approach_(i.e._MTBF)"><span id="Statistics-based_approach_.28i.e._MTBF.29"></span>Statistics-based approach (i.e. MTBF)</h4></div> <p>Reliability design begins with the development of a (system) <a href="/wiki/Mathematical_model" title="Mathematical model">model</a>. Reliability and availability models use <a href="/wiki/Block_diagram" title="Block diagram">block diagrams</a> and <a href="/wiki/Fault_Tree_Analysis" class="mw-redirect" title="Fault Tree Analysis">Fault Tree Analysis</a> to provide a graphical means of evaluating the relationships between different parts of the system. These models may incorporate predictions based on failure rates taken from historical data. While the (input data) predictions are often not accurate in an absolute sense, they are valuable to assess relative differences in design alternatives. Maintainability parameters, for example <a href="/wiki/Mean_time_to_repair" title="Mean time to repair">Mean time to repair</a> (MTTR), can also be used as inputs for such models. </p><p>The most important fundamental initiating causes and failure mechanisms are to be identified and analyzed with engineering tools. A diverse set of practical guidance as to performance and reliability should be provided to designers so that they can generate low-stressed designs and products that protect, or are protected against, damage and excessive wear. Proper validation of input loads (requirements) may be needed, in addition to verification for reliability "performance" by testing. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Fault_tree.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Fault_tree.svg/280px-Fault_tree.svg.png" decoding="async" width="280" height="296" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Fault_tree.svg/420px-Fault_tree.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Fault_tree.svg/560px-Fault_tree.svg.png 2x" data-file-width="660" data-file-height="698" /></a><figcaption>A fault tree diagram</figcaption></figure> <p>One of the most important design techniques is <a href="/wiki/Redundancy_(engineering)" title="Redundancy (engineering)">redundancy</a>. This means that if one part of the system fails, there is an alternate success path, such as a backup system. The reason why this is the ultimate design choice is related to the fact that high-confidence reliability evidence for new parts or systems is often not available, or is extremely expensive to obtain. By combining redundancy, together with a high level of failure monitoring, and the avoidance of common cause failures; even a system with relatively poor single-channel (part) reliability, can be made highly reliable at a system level (up to mission critical reliability). No testing of reliability has to be required for this. In conjunction with redundancy, the use of dissimilar designs or manufacturing processes (e.g. via different suppliers of similar parts) for single independent channels, can provide less sensitivity to quality issues (e.g. early childhood failures at a single supplier), allowing very-high levels of reliability to be achieved at all moments of the development cycle (from early life to long-term). Redundancy can also be applied in systems engineering by double checking requirements, data, designs, calculations, software, and tests to overcome systematic failures. </p><p>Another effective way to deal with reliability issues is to perform analysis that predicts degradation, enabling the prevention of unscheduled downtime events / failures. <a href="/wiki/Reliability_centered_maintenance" class="mw-redirect" title="Reliability centered maintenance">RCM</a> (Reliability Centered Maintenance) programs can be used for this. </p> <div class="mw-heading mw-heading4"><h4 id="Physics-of-failure-based_approach">Physics-of-failure-based approach</h4></div> <p>For electronic assemblies, there has been an increasing shift towards a different approach called <a href="/wiki/Physics_of_failure" title="Physics of failure">physics of failure</a>. This technique relies on understanding the physical static and dynamic failure mechanisms. It accounts for variation in load, strength, and stress that lead to failure with a high level of detail, made possible with the use of modern <a href="/wiki/Finite_element_method" title="Finite element method">finite element method</a> (FEM) software programs that can handle complex geometries and mechanisms such as creep, stress relaxation, fatigue, and probabilistic design (<a href="/wiki/Monte_Carlo_Methods" class="mw-redirect" title="Monte Carlo Methods">Monte Carlo Methods</a>/DOE). The material or component can be re-designed to reduce the probability of failure and to make it more robust against such variations. Another common design technique is component <a href="/wiki/Derating" title="Derating">derating</a>: i.e. selecting components whose specifications significantly exceed the expected stress levels, such as using heavier gauge electrical wire than might normally be specified for the expected <a href="/wiki/Electric_current" title="Electric current">electric current</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Common_tools_and_techniques">Common tools and techniques</h4></div> <p>Many of the tasks, techniques, and analyses used in Reliability Engineering are specific to particular industries and applications, but can commonly include: </p> <ul><li><a href="/wiki/Physics_of_failure" title="Physics of failure">Physics of failure</a> (PoF)</li> <li><a href="/wiki/Built-in_test" class="mw-redirect" title="Built-in test">Built-in self-test</a> (BIT or BIST) (testability analysis)</li> <li><a href="/wiki/Failure_mode_and_effects_analysis" title="Failure mode and effects analysis">Failure mode and effects analysis</a> (FMEA)</li> <li>Reliability <a href="/wiki/Hazard_analysis" title="Hazard analysis">hazard analysis</a></li> <li>Reliability block-diagram analysis</li> <li>Dynamic reliability block-diagram analysis<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Fault_tree_analysis" title="Fault tree analysis">Fault tree analysis</a></li> <li><a href="/wiki/Root_cause_analysis" title="Root cause analysis">Root cause analysis</a></li> <li>Statistical engineering, <a href="/wiki/Design_of_experiments" title="Design of experiments">design of experiments</a> – e.g. on simulations / FEM models or with testing</li> <li>Sneak circuit analysis</li> <li>Accelerated testing</li> <li>Reliability growth analysis (re-active reliability)</li> <li><a href="/wiki/Weibull_distribution" title="Weibull distribution">Weibull</a> analysis (for testing or mainly "re-active" reliability)</li> <li><a href="/wiki/Hypertabastic_survival_models" title="Hypertabastic survival models">Hypertabastic survival models</a></li> <li><a href="/wiki/Thermal_analysis" title="Thermal analysis">Thermal analysis</a> by finite element analysis (FEA) and / or measurement</li> <li>Thermal induced, shock and <a href="/wiki/Vibration_fatigue" title="Vibration fatigue">vibration fatigue</a> analysis by FEA and / or measurement</li> <li>Electromagnetic analysis</li> <li>Avoidance of <a href="/wiki/Single_point_of_failure" title="Single point of failure">single point of failure</a> (SPOF)</li> <li>Functional analysis and functional failure analysis (e.g., function FMEA, FHA or FFA)</li> <li>Predictive and preventive maintenance: reliability centered maintenance (RCM) analysis</li> <li>Testability analysis</li> <li>Failure diagnostics analysis (normally also incorporated in FMEA)</li> <li>Human error analysis</li> <li>Operational hazard analysis</li> <li><a href="/wiki/Maintenance#Preventive_maintenance" title="Maintenance">Preventative/Planned Maintenance</a> Optimization (PMO)</li> <li>Manual screening</li> <li><a href="/wiki/Integrated_logistics_support" title="Integrated logistics support">Integrated logistics support</a></li></ul> <p>Results from these methods are presented during reviews of part or system design, and logistics. Reliability is just one requirement among many for a complex part or system. Engineering trade-off studies are used to determine the <a href="/wiki/Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">optimum</a> balance between reliability requirements and other constraints. </p> <div class="mw-heading mw-heading3"><h3 id="The_importance_of_language">The importance of language</h3></div> <p>Reliability engineers, whether using quantitative or qualitative methods to describe a failure or hazard, rely on language to pinpoint the risks and enable issues to be solved. The language used must help create an orderly description of the function/item/system and its complex surrounding as it relates to the failure of these functions/items/systems. Systems engineering is very much about finding the correct words to describe the problem (and related risks), so that they can be readily solved via engineering solutions. Jack Ring said that a systems engineer's job is to "language the project." (Ring et al. 2000)<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> For part/system failures, reliability engineers should concentrate more on the "why and how", rather that predicting "when". Understanding "why" a failure has occurred (e.g. due to over-stressed components or manufacturing issues) is far more likely to lead to improvement in the designs and processes used<sup id="cite_ref-O'Connor_2002_4-1" class="reference"><a href="#cite_note-O'Connor_2002-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> than quantifying "when" a failure is likely to occur (e.g. via determining MTBF). To do this, first the reliability hazards relating to the part/system need to be classified and ordered (based on some form of qualitative and quantitative logic if possible) to allow for more efficient assessment and eventual improvement. This is partly done in pure language and <a href="/wiki/Proposition" title="Proposition">proposition</a> logic, but also based on experience with similar items. This can for example be seen in descriptions of events in <a href="/wiki/Fault_tree_analysis" title="Fault tree analysis">fault tree analysis</a>, <a href="/wiki/Failure_mode_and_effects_analysis" title="Failure mode and effects analysis">FMEA</a> analysis, and hazard (tracking) logs. In this sense language and proper grammar (part of qualitative analysis) plays an important role in reliability engineering, just like it does in <a href="/wiki/Safety_engineering" title="Safety engineering">safety engineering</a> or in-general within <a href="/wiki/Systems_engineering" title="Systems engineering">systems engineering</a>. </p><p>Correct use of language can also be key to identifying or reducing the risks of <a href="/wiki/Human_error" title="Human error">human error</a>, which are often the root cause of many failures. This can include proper instructions in maintenance manuals, operation manuals, emergency procedures, and others to prevent systematic human errors that may result in system failures. These should be written by trained or experienced technical authors using so-called simplified English or <a href="/wiki/Simplified_Technical_English" title="Simplified Technical English">Simplified Technical English</a>, where words and structure are specifically chosen and created so as to reduce ambiguity or risk of confusion (e.g. an "replace the old part" could ambiguously refer to a swapping a worn-out part with a non-worn-out part, or replacing a part with one using a more recent and hopefully improved design). </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_modeling">Reliability modeling</h2></div> <p>Reliability modeling is the process of predicting or understanding the reliability of a component or system prior to its implementation. Two types of analysis that are often used to model a complete system's <a href="/wiki/Availability" title="Availability">availability</a> behavior including effects from logistics issues like spare part provisioning, transport and manpower are fault tree analysis and <a href="/wiki/Reliability_block_diagram" title="Reliability block diagram">reliability block diagrams</a>. At a component level, the same types of analyses can be used together with others. The input for the models can come from many sources including testing; prior operational experience; field data; as well as data handbooks from similar or related industries. Regardless of source, all model input data must be used with great caution, as predictions are only valid in cases where the same product was used in the same context. As such, predictions are often only used to help compare alternatives. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Reliability_block_diagram.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Reliability_block_diagram.png/300px-Reliability_block_diagram.png" decoding="async" width="300" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Reliability_block_diagram.png/450px-Reliability_block_diagram.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Reliability_block_diagram.png/600px-Reliability_block_diagram.png 2x" data-file-width="1253" data-file-height="422" /></a><figcaption>A reliability block diagram showing a "1oo3" (1 out of 3) redundant designed subsystem</figcaption></figure> <p>For part level predictions, two separate fields of investigation are common: </p> <ul><li>The <a href="/wiki/Physics_of_failure" title="Physics of failure">physics of failure</a> approach uses an understanding of physical failure mechanisms involved, such as mechanical <a href="/wiki/Crack_propagation" class="mw-redirect" title="Crack propagation">crack propagation</a> or chemical <a href="/wiki/Corrosion" title="Corrosion">corrosion</a> degradation or failure;</li> <li>The <a href="/wiki/Parts_stress_modelling" title="Parts stress modelling">parts stress modelling</a> approach is an empirical method for prediction based on counting the number and type of components of the system, and the stress they undergo during operation.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Reliability_theory">Reliability theory</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Failure_rate" title="Failure rate">Failure rate</a> and <a href="/wiki/Survival_analysis" title="Survival analysis">Survival analysis</a></div> <p>Reliability is defined as the <a href="/wiki/Probability" title="Probability">probability</a> that a device will perform its intended function during a specified period of time under stated conditions. Mathematically, this may be expressed as, </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R(t)=Pr\{T>t\}=\int _{t}^{\infty }f(x)\,dx\ \!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>P</mi> <mi>r</mi> <mo fence="false" stretchy="false">{</mo> <mi>T</mi> <mo>></mo> <mi>t</mi> <mo fence="false" stretchy="false">}</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mtext> </mtext> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R(t)=Pr\{T>t\}=\int _{t}^{\infty }f(x)\,dx\ \!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cbbeac0ce7f9dfd12293c94109d1e486bd3dd8b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.574ex; height:5.843ex;" alt="{\displaystyle R(t)=Pr\{T>t\}=\int _{t}^{\infty }f(x)\,dx\ \!}"></span>, </p><p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08d6a18385bcf3e2edb3eb703484d2ebf1485b79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.166ex; width:4.197ex; height:2.843ex;" alt="{\displaystyle f(x)\!}"></span> is the failure <a href="/wiki/Probability_density_function" title="Probability density function">probability density function</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> is the length of the period of time (which is assumed to start from time zero). </p><p>There are a few key elements of this definition: </p> <ol><li>Reliability is predicated on "intended function:" Generally, this is taken to mean operation without failure. However, even if no individual part of the system fails, but the system as a whole does not do what was intended, then it is still charged against the system reliability. The system requirements specification is the criterion against which reliability is measured.</li> <li>Reliability applies to a specified period of time. In practical terms, this means that a system has a specified chance that it will operate without failure before time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/931cff7af09ba413dbc1cecdc4a3fa818a4c20b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T\!}"></span>. Reliability engineering ensures that components and materials will meet the requirements during the specified time. Note that units other than time may sometimes be used (e.g. "a mission", "operation cycles").</li> <li>Reliability is restricted to operation under stated (or explicitly defined) conditions. This constraint is necessary because it is impossible to design a system for unlimited conditions. A <a href="/wiki/Mars_rover" title="Mars rover">Mars rover</a> will have different specified conditions than a family car. The operating environment must be addressed during design and testing. That same rover may be required to operate in varying conditions requiring additional scrutiny.</li> <li>Two notable references on reliability theory and its mathematical and statistical foundations are Barlow, R. E. and Proschan, F. (1982) and Samaniego, F. J. (2007).</li></ol> <div class="mw-heading mw-heading3"><h3 id="Quantitative_system_reliability_parameters—theory"><span id="Quantitative_system_reliability_parameters.E2.80.94theory"></span>Quantitative system reliability parameters—theory</h3></div> <p>Quantitative requirements are specified using reliability <a href="/wiki/Parameter" title="Parameter">parameters</a>. The most common reliability parameter is the <a href="/wiki/Mean_time_to_failure" class="mw-redirect" title="Mean time to failure">mean time to failure</a> (MTTF), which can also be specified as the <a href="/wiki/Failure_rate" title="Failure rate">failure rate</a> (this is expressed as a frequency or conditional probability density function (PDF)) or the number of failures during a given period. These parameters may be useful for higher system levels and systems that are operated frequently (i.e. vehicles, machinery, and electronic equipment). Reliability increases as the MTTF increases. The MTTF is usually specified in hours, but can also be used with other units of measurement, such as miles or cycles. Using MTTF values on lower system levels can be very misleading, especially if they do not specify the associated Failures Modes and Mechanisms (The F in MTTF).<sup id="cite_ref-ReferenceA_17-1" class="reference"><a href="#cite_note-ReferenceA-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>In other cases, reliability is specified as the probability of mission success. For example, reliability of a scheduled aircraft flight can be specified as a dimensionless probability or a percentage, as often used in <a href="/wiki/System_safety" title="System safety">system safety</a> engineering. </p><p>A special case of mission success is the single-shot device or system. These are devices or systems that remain relatively dormant and only operate once. Examples include automobile <a href="/wiki/Airbags" class="mw-redirect" title="Airbags">airbags</a>, thermal <a href="/wiki/Battery_(electricity)" class="mw-redirect" title="Battery (electricity)">batteries</a> and <a href="/wiki/Missiles" class="mw-redirect" title="Missiles">missiles</a>. Single-shot reliability is specified as a probability of one-time success or is subsumed into a related parameter. Single-shot missile reliability may be specified as a requirement for the probability of a hit. For such systems, the <a href="/wiki/Safety_integrity_level" title="Safety integrity level">probability of failure on demand</a> (PFD) is the reliability measure – this is actually an "unavailability" number. The PFD is derived from failure rate (a frequency of occurrence) and mission time for non-repairable systems. </p><p>For repairable systems, it is obtained from failure rate, mean-time-to-repair (MTTR), and test interval. This measure may not be unique for a given system as this measure depends on the kind of demand. In addition to system level requirements, reliability requirements may be specified for critical subsystems. In most cases, reliability parameters are specified with appropriate statistical <a href="/wiki/Confidence_interval" title="Confidence interval">confidence intervals</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_testing">Reliability testing</h2></div> <p>The purpose of <b>reliability testing</b> or <b>reliability verification</b> is to discover potential problems with the design as early as possible and, ultimately, provide confidence that the system meets its reliability requirements. The reliability of the product in all environments such as expected use, transportation, or storage during the specified lifespan should be considered.<sup id="cite_ref-sciencedirect.com_10-1" class="reference"><a href="#cite_note-sciencedirect.com-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> It is to expose the product to natural or artificial environmental conditions to undergo its action to evaluate the performance of the product under the environmental conditions of actual use, transportation, and storage, and to analyze and study the degree of influence of environmental factors and their mechanism of action.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Through the use of various environmental test equipment to simulate the high temperature, low temperature, and high humidity, and temperature changes in the climate environment, to accelerate the reaction of the product in the use environment, to verify whether it reaches the expected quality in <a href="/wiki/R%26D" class="mw-redirect" title="R&D">R&D</a>, design, and manufacturing.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>Reliability verification is also called reliability testing, which refers to the use of modeling, statistics, and other methods to evaluate the reliability of the product based on the product's life span and expected performance.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Most product on the market requires reliability testing, such as automotive, <a href="/wiki/Integrated_circuit" title="Integrated circuit">integrated circuit</a>, heavy machinery used to mine nature resources, Aircraft auto software.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Reliability testing may be performed at several levels and there are different types of testing. Complex systems may be tested at component, circuit board, unit, assembly, subsystem and system levels.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> (The test level nomenclature varies among applications.) For example, performing <a href="/wiki/Environmental_stress_screening" title="Environmental stress screening">environmental stress screening</a> tests at lower levels, such as piece parts or small assemblies, catches problems before they cause failures at higher levels. Testing proceeds during each level of integration through full-up system testing, developmental testing, and operational testing, thereby reducing program risk. However, testing does not mitigate unreliability risk. </p><p>With each test both statistical <a href="/wiki/Type_I_and_type_II_errors" title="Type I and type II errors">type I and type II errors</a> could be made, depending on sample size, test time, assumptions and the needed discrimination ratio. There is risk of incorrectly rejecting a good design (type I error) and the risk of incorrectly accepting a bad design (type II error). </p><p>It is not always feasible to test all system requirements. Some systems are prohibitively expensive to test; some <a href="/wiki/Failure_mode" class="mw-redirect" title="Failure mode">failure modes</a> may take years to observe; some complex interactions result in a huge number of possible test cases; and some tests require the use of limited test ranges or other resources. In such cases, different approaches to testing can be used, such as (highly) accelerated life testing, <a href="/wiki/Design_of_experiments" title="Design of experiments">design of experiments</a>, and <a href="/wiki/Simulation" title="Simulation">simulations</a>. </p><p>The desired level of statistical confidence also plays a role in reliability testing. Statistical confidence is increased by increasing either the test time or the number of items tested. Reliability test plans are designed to achieve the specified reliability at the specified <a href="/wiki/Confidence_interval" title="Confidence interval">confidence level</a> with the minimum number of test units and test time. Different test plans result in different levels of risk to the producer and consumer. The desired reliability, statistical confidence, and risk levels for each side influence the ultimate test plan. The customer and developer should agree in advance on how reliability requirements will be tested. </p><p>A key aspect of reliability testing is to define "failure". Although this may seem obvious, there are many situations where it is not clear whether a failure is really the fault of the system. Variations in test conditions, operator differences, weather and unexpected situations create differences between the customer and the system developer. One strategy to address this issue is to use a scoring conference process. A scoring conference includes representatives from the customer, the developer, the test organization, the reliability organization, and sometimes independent observers. The scoring conference process is defined in the statement of work. Each test case is considered by the group and "scored" as a success or failure. This scoring is the official result used by the reliability engineer. </p><p>As part of the requirements phase, the reliability engineer develops a test strategy with the customer. The test strategy makes trade-offs between the needs of the reliability organization, which wants as much data as possible, and constraints such as cost, schedule and available resources. Test plans and procedures are developed for each reliability test, and results are documented. </p><p>Reliability testing is common in the Photonics industry. Examples of reliability tests of lasers are life test and <a href="/wiki/Burn-in" title="Burn-in">burn-in</a>. These tests consist of the highly accelerated aging, under controlled conditions, of a group of lasers. The data collected from these life tests are used to predict laser life expectancy under the intended operating characteristics.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Reliability_test_requirements">Reliability test requirements</h3></div> <p>There are many criteria to test depends on the product or process that are testing on, and mainly, there are five components that are most common:<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Product life span</li> <li>Intended function</li> <li>Operating Condition</li> <li>Probability of Performance</li> <li>User exceptions<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li></ol> <p>The product life span can be split into four different for analysis. Useful life is the estimated economic life of the product, which is defined as the time can be used before the cost of repair do not justify the continue use to the product. Warranty life is the product should perform the function within the specified time period. Design life is where during the design of the product, designer take into consideration on the life time of competitive product and customer desire and ensure that the product do not result in customer dissatisfaction.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>Reliability test requirements can follow from any analysis for which the first estimate of failure probability, failure mode or effect needs to be justified. Evidence can be generated with some level of confidence by testing. With software-based systems, the probability is a mix of software and hardware-based failures. Testing reliability requirements is problematic for several reasons. A single test is in most cases insufficient to generate enough statistical data. Multiple tests or long-duration tests are usually very expensive. Some tests are simply impractical, and environmental conditions can be hard to predict over a systems life-cycle. </p><p>Reliability engineering is used to design a realistic and affordable test program that provides empirical evidence that the system meets its reliability requirements. Statistical <a href="/wiki/Confidence_interval" title="Confidence interval">confidence levels</a> are used to address some of these concerns. A certain parameter is expressed along with a corresponding confidence level: for example, an <a href="/wiki/MTBF" class="mw-redirect" title="MTBF">MTBF</a> of 1000 hours at 90% confidence level. From this specification, the reliability engineer can, for example, design a test with explicit criteria for the number of hours and number of failures until the requirement is met or failed. Different sorts of tests are possible. </p><p>The combination of required reliability level and required confidence level greatly affects the development cost and the risk to both the customer and producer. Care is needed to select the best combination of requirements—e.g. cost-effectiveness. Reliability testing may be performed at various levels, such as component, <a href="/wiki/Subsystem" class="mw-redirect" title="Subsystem">subsystem</a> and <a href="/wiki/System" title="System">system</a>. Also, many factors must be addressed during testing and operation, such as extreme temperature and humidity, shock, vibration, or other environmental factors (like loss of signal, cooling or power; or other catastrophes such as fire, floods, excessive heat, physical or security violations or other myriad forms of damage or degradation). For systems that must last many years, accelerated life tests may be needed. </p> <div class="mw-heading mw-heading3"><h3 id="Testing_method">Testing method</h3></div> <p>A systematic approach to reliability testing is to, first, determine reliability goal, then do tests that are linked to performance and determine the reliability of the product.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> A reliability verification test in modern industries should clearly determine how they relate to the product's overall reliability performance and how individual tests impact the warranty cost and customer satisfaction.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Accelerated_testing">Accelerated testing</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Accelerated_life_testing" title="Accelerated life testing">Accelerated life testing</a></div> <p>The purpose of <a href="/wiki/Accelerated_life_testing" title="Accelerated life testing">accelerated life testing (ALT test)</a> is to induce field failure in the laboratory at a much faster rate by providing a harsher, but nonetheless representative, environment. In such a test, the product is expected to fail in the lab just as it would have failed in the field—but in much less time. The main objective of an accelerated test is either of the following: </p> <ul><li>To discover failure modes</li> <li>To predict the normal field life from the high <a href="/wiki/Stress_testing" title="Stress testing">stress</a> lab life</li></ul> <p>An accelerated testing program can be broken down into the following steps: </p> <ul><li>Define objective and scope of the test</li> <li>Collect required information about the product</li> <li>Identify the stress(es)</li> <li>Determine level of stress(es)</li> <li>Conduct the accelerated test and analyze the collected data.</li></ul> <p>Common ways to determine a life stress relationship are: </p> <ul><li>Arrhenius model</li> <li>Eyring model</li> <li>Inverse power law model</li> <li>Temperature–humidity model</li> <li>Temperature non-thermal model</li></ul> <div class="mw-heading mw-heading2"><h2 id="Software_reliability">Software reliability</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Software_quality" title="Software quality">Software quality</a> and <a href="/wiki/Site_reliability_engineering" title="Site reliability engineering">Site reliability engineering</a></div> <p>Software reliability is a special aspect of reliability engineering. It focuses on foundations and techniques to make software more reliable, i.e., resilient to faults. System reliability, by definition, includes all parts of the system, including hardware, software, supporting infrastructure (including critical external interfaces), operators and procedures. Traditionally, reliability engineering focuses on critical hardware parts of the system. Since the widespread use of digital <a href="/wiki/Integrated_circuit" title="Integrated circuit">integrated circuit</a> technology, software has become an increasingly critical part of most electronics and, hence, nearly all present day systems. Therefore, software reliability has gained prominence within the field of system reliability. </p><p>There are significant differences, however, in how software and hardware behave. Most hardware unreliability is the result of a component or material failure that results in the system not performing its intended function. Repairing or replacing the hardware component restores the system to its original operating state. However, software does not fail in the same sense that hardware fails. Instead, software unreliability is the result of unanticipated results of software operations. Even relatively small software programs can have astronomically large <a href="/wiki/Combinations" class="mw-redirect" title="Combinations">combinations</a> of inputs and states that are infeasible to exhaustively test. Restoring software to its original state only works until the same combination of inputs and states results in the same unintended result. Software reliability engineering must take this into account. </p><p>Despite this difference in the source of failure between software and hardware, several <a href="/wiki/List_of_software_reliability_models" title="List of software reliability models">software reliability models</a> based on statistics have been proposed to quantify what we experience with software: the longer software is run, the higher the probability that it will eventually be used in an untested manner and exhibit a latent defect that results in a failure (<a href="/w/index.php?title=Shooman&action=edit&redlink=1" class="new" title="Shooman (page does not exist)">Shooman</a> 1987), (Musa 2005), (Denney 2005). </p><p>As with hardware, software reliability depends on good requirements, design and implementation. Software reliability engineering relies heavily on a disciplined <a href="/wiki/Software_engineering" title="Software engineering">software engineering</a> process to anticipate and design against <a href="/wiki/Unintended_consequence" class="mw-redirect" title="Unintended consequence">unintended consequences</a>. There is more overlap between software <a href="/wiki/Quality_assurance" title="Quality assurance">quality engineering</a> and software reliability engineering than between hardware quality and reliability. A good software development plan is a key aspect of the software reliability program. The software development plan describes the design and coding standards, <a href="/wiki/Software_peer_review" title="Software peer review">peer reviews</a>, <a href="/wiki/Unit_test" class="mw-redirect" title="Unit test">unit tests</a>, <a href="/wiki/Configuration_management" title="Configuration management">configuration management</a>, <a href="/wiki/Software_metrics" class="mw-redirect" title="Software metrics">software metrics</a> and software models to be used during software development. </p><p>A common reliability metric is the number of software faults per line of code (FLOC), usually expressed as faults per thousand lines of code. This metric, along with software execution time, is key to most software reliability models and estimates. The theory is that the software reliability increases as the number of faults (or fault density) decreases. Establishing a direct connection between fault density and mean-time-between-failure is difficult, however, because of the way software faults are distributed in the code, their severity, and the probability of the combination of inputs necessary to encounter the fault. Nevertheless, fault density serves as a useful indicator for the reliability engineer. Other software metrics, such as complexity, are also used. This metric remains controversial, since changes in software development and verification practices can have dramatic impact on overall defect rates. </p><p><a href="/wiki/Software_testing" title="Software testing">Software testing</a> is an important aspect of software reliability. Even the best software development process results in some software faults that are nearly undetectable until tested. Software is tested at several levels, starting with individual <a href="/wiki/Unit_testing" title="Unit testing">units</a>, through <a href="/wiki/Integration_testing" title="Integration testing">integration</a> and full-up <a href="/wiki/System_testing" title="System testing">system testing</a>. All phases of testing, software faults are discovered, corrected, and re-tested. Reliability estimates are updated based on the fault density and other metrics. At a system level, mean-time-between-failure data can be collected and used to estimate reliability. Unlike hardware, performing exactly the same test on exactly the same software configuration does not provide increased statistical confidence. Instead, software reliability uses different metrics, such as <a href="/wiki/Code_coverage" title="Code coverage">code coverage</a>. </p><p>The Software Engineering Institute's <a href="/wiki/Capability_maturity_model" class="mw-redirect" title="Capability maturity model">capability maturity model</a> is a common means of assessing the overall software development process for reliability and quality purposes. </p> <div class="mw-heading mw-heading2"><h2 id="Structural_reliability">Structural reliability</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Structural_reliability" title="Structural reliability">Structural reliability</a></div> <p><a href="/wiki/Structural_reliability" title="Structural reliability">Structural reliability</a> or the reliability of structures is the application of reliability theory to the behavior of <a href="/wiki/Building" title="Building">structures</a>. It is used in both the design and maintenance of different types of structures including concrete and steel structures.<sup id="cite_ref-:1_38-0" class="reference"><a href="#cite_note-:1-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> In structural reliability studies both loads and resistances are modeled as probabilistic variables. Using this approach the probability of failure of a structure is calculated. </p> <div class="mw-heading mw-heading2"><h2 id="Comparison_to_safety_engineering">Comparison to safety engineering</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Safety_engineering" title="Safety engineering">Safety engineering</a></div> <p>Reliability for safety and reliability for availability are often closely related. Lost availability of an engineering system can cost money. If a subway system is unavailable the subway operator will lose money for each hour the system is down. The subway operator will lose more money if safety is compromised. The definition of reliability is tied to a probability of not encountering a failure. A failure can cause loss of safety, loss of availability or both. It is undesirable to lose safety or availability in a critical system. </p><p>Reliability engineering is concerned with overall minimisation of failures that could lead to financial losses for the responsible entity, whereas <a href="/wiki/Safety_engineering" title="Safety engineering">safety engineering</a> focuses on minimising a specific set of failure types that in general could lead to loss of life, injury or damage to equipment. </p><p>Reliability hazards could transform into incidents leading to a loss of revenue for the company or the customer, for example due to direct and indirect costs associated with: loss of production due to system unavailability; unexpected high or low demands for spares; repair costs; man-hours; re-designs or interruptions to normal production.<sup id="cite_ref-Verma,_Ajit_Kumar_2010_40-0" class="reference"><a href="#cite_note-Verma,_Ajit_Kumar_2010-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p><p>Safety engineering is often highly specific, relating only to certain tightly regulated industries, applications, or areas. It primarily focuses on system safety hazards that could lead to severe accidents including: loss of life; destruction of equipment; or environmental damage. As such, the related system functional reliability requirements are often extremely high. Although it deals with unwanted failures in the same sense as reliability engineering, it, however, has less of a focus on direct costs, and is not concerned with post-failure repair actions. Another difference is the level of impact of failures on society, leading to a tendency for strict control by governments or regulatory bodies (e.g. nuclear, aerospace, defense, rail and oil industries).<sup id="cite_ref-Verma,_Ajit_Kumar_2010_40-1" class="reference"><a href="#cite_note-Verma,_Ajit_Kumar_2010-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Fault_tolerance">Fault tolerance</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Fault_tolerance" title="Fault tolerance">Fault tolerance</a></div> <p>Safety can be increased using a 2oo2 cross checked redundant system. Availability can be increased by using "1oo2" (1 out of 2) redundancy at a part or system level. If both redundant elements disagree the more permissive element will maximize availability. A 1oo2 system should never be relied on for safety. Fault-tolerant systems often rely on additional redundancy (e.g. <a href="/wiki/Triple_modular_redundancy" title="Triple modular redundancy">2oo3 voting logic</a>) where multiple redundant elements must agree on a potentially unsafe action before it is performed. This increases both availability and safety at a system level. This is common practice in aerospace systems that need continued availability and do not have a <a href="/wiki/Fail-safe" title="Fail-safe">fail-safe</a> mode. For example, aircraft may use triple modular redundancy for <a href="/wiki/Flight_computer" title="Flight computer">flight computers</a> and control surfaces (including occasionally different modes of operation e.g. electrical/mechanical/hydraulic) as these need to always be operational, due to the fact that there are no "safe" default positions for control surfaces such as rudders or ailerons when the aircraft is flying. </p> <div class="mw-heading mw-heading3"><h3 id="Basic_reliability_and_mission_reliability">Basic reliability and mission reliability</h3></div> <p>The above example of a 2oo3 fault tolerant system increases both mission reliability as well as safety. However, the "basic" reliability of the system will in this case still be lower than a non-redundant (1oo1) or 2oo2 system. Basic reliability engineering covers all failures, including those that might not result in system failure, but do result in additional cost due to: maintenance repair actions; logistics; spare parts etc. For example, replacement or repair of 1 faulty channel in a 2oo3 voting system, (the system is still operating, although with one failed channel it has actually become a 2oo2 system) is contributing to basic unreliability but not mission unreliability. As an example, the failure of the tail-light of an aircraft will not prevent the plane from flying (and so is not considered a mission failure), but it does need to be remedied (with a related cost, and so does contribute to the basic unreliability levels). </p> <div class="mw-heading mw-heading3"><h3 id="Detectability_and_common_cause_failures">Detectability and common cause failures</h3></div> <p>When using fault tolerant (redundant) systems or systems that are equipped with protection functions, detectability of failures and avoidance of common cause failures becomes paramount for safe functioning and/or mission reliability. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_versus_quality_(Six_Sigma)"><span id="Reliability_versus_quality_.28Six_Sigma.29"></span>Reliability versus quality (Six Sigma)</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Six_Sigma" title="Six Sigma">Six Sigma</a></div> <p>Quality often focuses on manufacturing defects during the warranty phase. Reliability looks at the failure intensity over the whole life of a product or engineering system from commissioning to decommissioning. <a href="/wiki/Six_Sigma" title="Six Sigma">Six Sigma</a> has its roots in statistical control in quality of manufacturing. Reliability engineering is a specialty part of systems engineering. The systems engineering process is a discovery process that is often unlike a manufacturing process. A manufacturing process is often focused on repetitive activities that achieve high quality outputs with minimum cost and time.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p><p>The everyday usage term "quality of a product" is loosely taken to mean its inherent degree of excellence. In industry, a more precise definition of quality as "conformance to requirements or specifications at the start of use" is used. Assuming the final product specification adequately captures the original requirements and customer/system needs, the quality level can be measured as the fraction of product units shipped that meet specifications.<sup id="cite_ref-itl.nist.gov_42-0" class="reference"><a href="#cite_note-itl.nist.gov-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> Manufactured goods quality often focuses on the number of warranty claims during the warranty period. </p><p>Quality is a snapshot at the start of life through the warranty period and is related to the control of lower-level product specifications. This includes time-zero defects i.e. where manufacturing mistakes escaped final Quality Control. In theory the quality level might be described by a single fraction of defective products. Reliability, as a part of systems engineering, acts as more of an ongoing assessment of failure rates over many years. Theoretically, all items will fail over an infinite period of time.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> Defects that appear over time are referred to as reliability fallout. To describe reliability fallout a probability model that describes the fraction fallout over time is needed. This is known as the life distribution model.<sup id="cite_ref-itl.nist.gov_42-1" class="reference"><a href="#cite_note-itl.nist.gov-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> Some of these reliability issues may be due to inherent design issues, which may exist even though the product conforms to specifications. Even items that are produced perfectly will fail over time due to one or more failure mechanisms (e.g. due to human error or mechanical, electrical, and chemical factors). These reliability issues can also be influenced by acceptable levels of variation during initial production. </p><p>Quality and reliability are, therefore, related to manufacturing. Reliability is more targeted towards clients who are focused on failures throughout the whole life of the product such as the military, airlines or railroads. Items that do not conform to product specification will generally do worse in terms of reliability (having a lower MTTF), but this does not always have to be the case. The full mathematical quantification (in statistical models) of this combined relation is in general very difficult or even practically impossible. In cases where manufacturing variances can be effectively reduced, six sigma tools have been shown to be useful to find optimal process solutions which can increase quality and reliability. Six Sigma may also help to design products that are more robust to manufacturing induced failures and infant mortality defects in engineering systems and manufactured product. </p><p>In contrast with Six Sigma, reliability engineering solutions are generally found by focusing on reliability testing and system design. Solutions are found in different ways, such as by simplifying a system to allow more of the mechanisms of failure involved to be understood; performing detailed calculations of material stress levels allowing suitable safety factors to be determined; finding possible abnormal system load conditions and using this to increase robustness of a design to manufacturing variance related failure mechanisms. Furthermore, reliability engineering uses system-level solutions, like designing redundant and fault-tolerant systems for situations with high availability needs (see <a href="#Vs_Safety_engineering">Reliability engineering vs Safety engineering</a> above). </p><p>Note: A "defect" in six-sigma/quality literature is not the same as a "failure" (Field failure | e.g. fractured item) in reliability. A six-sigma/quality defect refers generally to non-conformance with a requirement (e.g. basic functionality or a key dimension). Items can, however, fail over time, even if these requirements are all fulfilled. Quality is generally not concerned with asking the crucial question "are the requirements actually correct?", whereas reliability is. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_operational_assessment">Reliability operational assessment</h2></div> <p>Once systems or parts are being produced, reliability engineering attempts to monitor, assess, and correct deficiencies. Monitoring includes electronic and visual surveillance of critical parameters identified during the fault tree analysis design stage. Data collection is highly dependent on the nature of the system. Most large organizations have <a href="/wiki/Quality_control" title="Quality control">quality control</a> groups that collect failure data on vehicles, equipment and machinery. Consumer product failures are often tracked by the number of returns. For systems in dormant storage or on standby, it is necessary to establish a formal surveillance program to inspect and test random samples. Any changes to the system, such as field upgrades or recall repairs, require additional reliability testing to ensure the reliability of the modification. Since it is not possible to anticipate all the failure modes of a given system, especially ones with a human element, failures will occur. The reliability program also includes a systematic <a href="/wiki/Root_cause_analysis" title="Root cause analysis">root cause analysis</a> that identifies the causal relationships involved in the failure such that effective corrective actions may be implemented. When possible, system failures and corrective actions are reported to the reliability engineering organization. </p><p>Some of the most common methods to apply to a reliability operational assessment are <a href="/wiki/Failure_reporting,_analysis,_and_corrective_action_system" title="Failure reporting, analysis, and corrective action system">failure reporting, analysis, and corrective action systems</a> (FRACAS). This systematic approach develops a reliability, safety, and logistics assessment based on failure/incident reporting, management, analysis, and corrective/preventive actions. Organizations today are adopting this method and utilizing commercial systems (such as Web-based FRACAS applications) that enable them to create a failure/incident data repository from which statistics can be derived to view accurate and genuine reliability, safety, and quality metrics. </p><p>It is extremely important for an organization to adopt a common FRACAS system for all end items. Also, it should allow test results to be captured in a practical way. Failure to adopt one easy-to-use (in terms of ease of data-entry for field engineers and repair shop engineers) and easy-to-maintain integrated system is likely to result in a failure of the FRACAS program itself. </p><p>Some of the common outputs from a FRACAS system include Field MTBF, MTTR, spares consumption, reliability growth, failure/incidents distribution by type, location, part no., serial no., and symptom. </p><p>The use of past data to predict the reliability of new comparable systems/items can be misleading as reliability is a function of the context of use and can be affected by small changes in design/manufacturing. </p> <div class="mw-heading mw-heading2"><h2 id="Reliability_organizations">Reliability organizations</h2></div> <p>Systems of any significant complexity are developed by organizations of people, such as a commercial <a href="/wiki/Company_(law)" class="mw-redirect" title="Company (law)">company</a> or a <a href="/wiki/Government" title="Government">government</a> agency. The reliability engineering organization must be consistent with the company's <a href="/wiki/Organizational_structure" title="Organizational structure">organizational structure</a>. For small, non-critical systems, reliability engineering may be informal. As complexity grows, the need arises for a formal reliability function. Because reliability is important to the customer, the customer may even specify certain aspects of the reliability organization. </p><p>There are several common types of reliability organizations. The project manager or chief engineer may employ one or more reliability engineers directly. In larger organizations, there is usually a product assurance or <a href="/wiki/Specialty_engineering" title="Specialty engineering">specialty engineering</a> organization, which may include reliability, <a href="/wiki/Maintainability" title="Maintainability">maintainability</a>, <a href="/wiki/Quality_(business)" title="Quality (business)">quality</a>, safety, <a href="/wiki/Human_factors" class="mw-redirect" title="Human factors">human factors</a>, <a href="/wiki/Logistics" title="Logistics">logistics</a>, etc. In such case, the reliability engineer reports to the product assurance manager or specialty engineering manager. </p><p>In some cases, a company may wish to establish an independent reliability organization. This is desirable to ensure that the system reliability, which is often expensive and time-consuming, is not unduly slighted due to budget and schedule pressures. In such cases, the reliability engineer works for the project day-to-day, but is actually employed and paid by a separate organization within the company. </p><p>Because reliability engineering is critical to early system design, it has become common for reliability engineers, however, the organization is structured, to work as part of an <a href="/wiki/Integrated_product_team" title="Integrated product team">integrated product team</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Education">Education</h2></div> <p>Some universities offer graduate degrees in reliability engineering. Other reliability professionals typically have a physics degree from a university or college program. Many engineering programs offer reliability courses, and some universities have entire reliability engineering programs. A reliability engineer must be registered as a <a href="/wiki/Professional_engineer" class="mw-redirect" title="Professional engineer">professional engineer</a> by the state or province by law, but not all reliability professionals are engineers. Reliability engineers are required in systems where public safety is at risk. There are many professional conferences and industry training programs available for reliability engineers. Several professional organizations exist for reliability engineers, including the American Society for Quality Reliability Division (ASQ-RD),<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> the <a href="/wiki/IEEE_Reliability_Society" class="mw-redirect" title="IEEE Reliability Society">IEEE Reliability Society</a>, the <a href="/wiki/American_Society_for_Quality" title="American Society for Quality">American Society for Quality</a> (ASQ),<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> and the Society of Reliability Engineers (SRE).<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <style data-mw-deduplicate="TemplateStyles:r1259569809">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_kcmsystem.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Nuvola_apps_kcmsystem.svg/28px-Nuvola_apps_kcmsystem.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Nuvola_apps_kcmsystem.svg/42px-Nuvola_apps_kcmsystem.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Nuvola_apps_kcmsystem.svg/56px-Nuvola_apps_kcmsystem.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Engineering" title="Portal:Engineering">Engineering portal</a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Dependability" title="Dependability">Dependability</a> – Measure in systems engineering</li> <li><a href="/wiki/Durable_good" title="Durable good">Durable good</a> – Good that has long term use</li> <li><a href="/wiki/Factor_of_safety" title="Factor of safety">Factor of safety</a> – System strength beyond intended load</li> <li><a href="/wiki/Failing_badly" title="Failing badly">Failing badly</a> – Fails with a catastrophic result or without warning</li> <li><a href="/wiki/Failure_mode_and_effects_analysis" title="Failure mode and effects analysis">Failure mode and effects analysis</a> (<abbr>FMEA</abbr>) – Analysis of potential system failures</li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a> – Study of propagation of cracks in materials</li> <li><a href="/wiki/Highly_accelerated_life_test" title="Highly accelerated life test">Highly accelerated life test</a> – Stress testing methodology for enhancing product reliability</li> <li><a href="/wiki/Highly_accelerated_stress_test" title="Highly accelerated stress test">Highly accelerated stress test</a></li> <li><a href="/wiki/Human_reliability" title="Human reliability">Human reliability</a> – Factor in safety, ergonomics and system resilience</li> <li><a href="/wiki/Industrial_engineering" title="Industrial engineering">Industrial engineering</a> – Branch of engineering which deals with the optimization of complex processes or systems</li> <li><a href="/wiki/Institute_of_Industrial_and_Systems_Engineers" title="Institute of Industrial and Systems Engineers">Institute of Industrial and Systems Engineers</a> – Professional society for the support of the industrial engineering profession</li> <li><a href="/wiki/Logistics_engineering" title="Logistics engineering">Logistics engineering</a> – Field of engineering</li> <li><a href="/wiki/Performance_engineering" title="Performance engineering">Performance engineering</a> – Encompasses the techniques applied during a systems development life cycle and <a href="/wiki/Performance_indicator" title="Performance indicator">Performance indicator</a> – Measurement that evaluates the success of an organization</li> <li><a href="/wiki/Product_certification" title="Product certification">Product certification</a> – Performance and quality assurance</li> <li><a href="/wiki/Product_testing" title="Product testing">Product testing</a> – Line of work testing consumer products</li> <li><a href="/wiki/Overall_equipment_effectiveness" title="Overall equipment effectiveness">Overall equipment effectiveness</a> – Measure of how well a manufacturing operation is utilized</li> <li><a href="/wiki/RAMS" class="mw-redirect" title="RAMS">RAMS</a> – Engineering characterization of a product or system<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Reliability,_availability_and_serviceability" title="Reliability, availability and serviceability">Reliability, availability and serviceability</a> – Quality of robustness of computer hardware</li> <li><a href="/wiki/Reliability_theory_of_aging_and_longevity" title="Reliability theory of aging and longevity">Reliability theory of aging and longevity</a> – Biophysics theory</li> <li><a href="/wiki/Risk-based_inspection" title="Risk-based inspection">Risk-based inspection</a> – an Optimal maintenance business process used to examine equipment such as pressure vessels, heat exchangers and piping in industrial plants<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Robustness_validation" title="Robustness validation">Robustness validation</a></li> <li><a href="/wiki/Security_engineering" title="Security engineering">Security engineering</a> – Process of incorporating security controls into an information system</li> <li><a href="/wiki/Software_reliability_testing" title="Software reliability testing">Software reliability testing</a></li> <li><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a> – Branch of mechanics concerned with solid materials and their behaviors</li> <li><a href="/wiki/Spurious_trip_level" title="Spurious trip level">Spurious trip level</a> – measure of the spurious activations of a safety or alarm system<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Strength_of_materials" title="Strength of materials">Strength of materials</a> – Behavior of solid objects subject to stresses and strains</li> <li><a href="/wiki/Stress%E2%80%93strength_analysis" title="Stress–strength analysis">Stress–strength analysis</a> – tool in reliability engineering; analysis of the strength of the materials and the interference of the stresses placed on the materials, where "materials" is not necessarily the raw goods or parts, but can be an entire system<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Structural_fracture_mechanics" title="Structural fracture mechanics">Structural fracture mechanics</a> – Field of structural engineering</li> <li><a href="/wiki/Temperature_cycling" title="Temperature cycling">Temperature cycling</a> – Chemical process</li> <li><a href="/wiki/Weibull_distribution" title="Weibull distribution">Weibull distribution</a> – Continuous probability distribution</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> 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style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://asq.org/quality-resources/reliability">"American Society for Quality"</a>. <i>American Society for Quality</i>. 24 July 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=American+Society+for+Quality&rft.atitle=American+Society+for+Quality&rft.date=2024-07-24&rft_id=https%3A%2F%2Fasq.org%2Fquality-resources%2Freliability&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReliability+engineering" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a 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Wang, Yinglong; Guo, Ying; Jiang, Mingyue (19 February 2019). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6380623">"A metamorphic testing approach for event sequences"</a>. <i>PLOS ONE</i>. <b>14</b> (2): e0212476. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019PLoSO..1412476C">2019PLoSO..1412476C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pone.0212476">10.1371/journal.pone.0212476</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1932-6203">1932-6203</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6380623">6380623</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/30779769">30779769</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PLOS+ONE&rft.atitle=A+metamorphic+testing+approach+for+event+sequences&rft.volume=14&rft.issue=2&rft.pages=e0212476&rft.date=2019-02-19&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6380623%23id-name%3DPMC&rft_id=info%3Abibcode%2F2019PLoSO..1412476C&rft_id=info%3Apmid%2F30779769&rft_id=info%3Adoi%2F10.1371%2Fjournal.pone.0212476&rft.issn=1932-6203&rft.aulast=Chen&rft.aufirst=Jing&rft.au=Wang%2C+Yinglong&rft.au=Guo%2C+Ying&rft.au=Jiang%2C+Mingyue&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6380623&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReliability+engineering" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBieńkowskaTworekZabłocka-Kluczka2020" class="citation journal cs1">Bieńkowska, Agnieszka; 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Quality versus reliability"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=8.1.1.1.+Quality+versus+reliability&rft_id=http%3A%2F%2Fwww.itl.nist.gov%2Fdiv898%2Fhandbook%2Fapr%2Fsection1%2Fapr111.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReliability+engineering" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.talkorigins.org/faqs/thermo/probability.html">"The Second Law of Thermodynamics, Evolution, and Probability"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Second+Law+of+Thermodynamics%2C+Evolution%2C+and+Probability&rft_id=http%3A%2F%2Fwww.talkorigins.org%2Ffaqs%2Fthermo%2Fprobability.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReliability+engineering" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://asqrd.org">American Society for Quality Reliability Division (ASQ-RD)</a></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://asq.org/cert/reliability-engineer">American Society for Quality (ASQ)</a></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.sre.org">Society of Reliability Engineers (SRE)</a></span> </li> </ol></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFN._Diaz,_R._Pascual,_F._Ruggeri,_E._López_Droguett2017" class="citation journal cs1">N. Diaz, R. Pascual, F. Ruggeri, E. López Droguett (2017). 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E. and Proscan, F. (1981) Statistical Theory of Reliability and Life Testing, To Begin With Press, Silver Springs, MD.</li> <li><a rel="nofollow" class="external text" href="https://medium.com/@erangadarora/cracking-the-weibull-code-understanding-failure-patterns-with-easy-intution-e0c64dec7a42">Simplifying Hardware Reliability : Intuitive Insights into the Weibull Distribution in less than 5 min ! ..(with Python Code)</a></li> <li>Blanchard, Benjamin S. (1992), <i>Logistics Engineering and Management</i> (Fourth Ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey.</li> <li>Breitler, Alan L. and Sloan, C. (2005), Proceedings of the American Institute of Aeronautics and Astronautics (AIAA) Air Force T&E Days Conference, Nashville, TN, December, 2005: System Reliability Prediction: towards a General Approach Using a Neural Network.</li> <li>Ebeling, Charles E., (1997), <i>An Introduction to Reliability and Maintainability Engineering</i>, McGraw-Hill Companies, Inc., Boston.</li> <li>Denney, Richard (2005) Succeeding with Use Cases: Working Smart to Deliver Quality. Addison-Wesley Professional Publishing. ISBN. Discusses the use of software reliability engineering in <a href="/wiki/Use_case" title="Use case">use case</a> driven software development.</li> <li>Gano, Dean L. (2007), "Apollo Root Cause Analysis" (Third Edition), Apollonian Publications, LLC., Richland, Washington</li> <li><a href="/wiki/Oliver_Wendell_Holmes_Sr." title="Oliver Wendell Holmes Sr.">Holmes, Oliver Wendell</a> Sr. <a href="https://en.wikisource.org/wiki/The_Deacon%27s_Masterpiece" class="extiw" title="s:The Deacon's Masterpiece">The Deacon's Masterpiece</a></li> <li>Horsburgh, Peter (2018), "5 Habits of an Extraordinary Reliability Engineer", Reliability Web</li> <li>Kapur, K.C., and Lamberson, L.R., (1977), <i>Reliability in Engineering Design</i>, John Wiley & Sons, New York.</li> <li>Kececioglu, Dimitri, (1991) "Reliability Engineering Handbook", Prentice-Hall, Englewood Cliffs, New Jersey</li> <li><a href="/wiki/Trevor_Kletz" title="Trevor Kletz">Trevor Kletz</a> (1998) <i>Process Plants: A Handbook for Inherently Safer Design</i> CRC <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-56032-619-0" title="Special:BookSources/1-56032-619-0">1-56032-619-0</a></li> <li>Leemis, Lawrence, (1995) <i>Reliability: Probabilistic Models and Statistical Methods</i>, 1995, Prentice-Hall. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-720517-1" title="Special:BookSources/0-13-720517-1">0-13-720517-1</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLees2005" class="citation book cs1"><a href="/wiki/Frank_Lees" title="Frank Lees">Lees, Frank</a> (2005). <i>Loss Prevention in the Process Industries</i> (3rd ed.). Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7506-7555-0" title="Special:BookSources/978-0-7506-7555-0"><bdi>978-0-7506-7555-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Loss+Prevention+in+the+Process+Industries&rft.edition=3rd&rft.pub=Elsevier&rft.date=2005&rft.isbn=978-0-7506-7555-0&rft.aulast=Lees&rft.aufirst=Frank&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReliability+engineering" class="Z3988"></span></li> <li>MacDiarmid, Preston; Morris, Seymour; et al., (1995), <i>Reliability Toolkit: Commercial Practices Edition</i>, Reliability Analysis Center and Rome Laboratory, Rome, New York.</li> <li><a href="/wiki/Mohammad_Modarres" title="Mohammad Modarres">Modarres, Mohammad</a>; Kaminskiy, Mark; <a href="/wiki/Vasiliy_Krivtsov" class="mw-redirect" title="Vasiliy Krivtsov">Krivtsov</a>, <a href="/wiki/Vasiliy_Krivtsov" class="mw-redirect" title="Vasiliy Krivtsov">Vasiliy</a> (1999), <i><a href="/wiki/Reliability_Engineering_and_Risk_Analysis:_A_Practical_Guide" class="mw-redirect" title="Reliability Engineering and Risk Analysis: A Practical Guide">Reliability Engineering and Risk Analysis: A Practical Guide</a></i>, CRC Press, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-2000-8" title="Special:BookSources/0-8247-2000-8">0-8247-2000-8</a>.</li> <li>Musa, John (2005) Software Reliability Engineering: More Reliable Software Faster and Cheaper, 2nd. Edition, AuthorHouse. ISBN</li> <li>Neubeck, Ken (2004) "Practical Reliability Analysis", Prentice Hall, New Jersey</li> <li>Neufelder, Ann Marie, (1993), <i>Ensuring Software Reliability</i>, Marcel Dekker, Inc., New York.</li> <li>O'Connor, Patrick D. T. (2002), <i>Practical Reliability Engineering</i> (Fourth Ed.), John Wiley & Sons, New York. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-4708-4462-5" title="Special:BookSources/978-0-4708-4462-5">978-0-4708-4462-5</a>.</li> <li>Samaniego, Francisco J. (2007) "System Signatures and their Applications in Engineering Reliability", Springer (International Series in Operations Research and Management Science), New York.</li> <li>Shooman, Martin, (1987), <i>Software Engineering: Design, Reliability, and Management</i>, McGraw-Hill, New York.</li> <li>Tobias, Trindade, (1995), <i>Applied Reliability</i>, Chapman & Hall/CRC, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-442-00469-9" title="Special:BookSources/0-442-00469-9">0-442-00469-9</a></li> <li><a rel="nofollow" class="external text" href="https://www.springer.com/series/6917">Springer Series in Reliability Engineering</a></li> <li>Nelson, Wayne B., (2004), <i>Accelerated Testing—Statistical Models, Test Plans, and Data Analysis</i>, John Wiley & Sons, New York, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-69736-2" title="Special:BookSources/0-471-69736-2">0-471-69736-2</a></li> <li>Bagdonavicius, V., Nikulin, M., (2002), "Accelerated Life Models. Modeling and Statistical analysis", CHAPMAN&HALL/CRC, Boca Raton, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-58488-186-0" title="Special:BookSources/1-58488-186-0">1-58488-186-0</a></li> <li>Todinov, M. (2016), "Reliability and Risk Models: setting reliability requirements", Wiley, 978-1-118-87332-8.</li></ul> <div class="mw-heading mw-heading3"><h3 id="US_standards,_specifications,_and_handbooks"><span id="US_standards.2C_specifications.2C_and_handbooks"></span>US standards, specifications, and handbooks</h3></div> <ul><li><a rel="nofollow" class="external text" href="http://www.everyspec.com/USAF/TORs/TOR2007-8583-6889_14232/">Aerospace Report Number: TOR-2007(8583)-6889</a> <i>Reliability Program Requirements for Space Systems</i>, <a href="/wiki/The_Aerospace_Corporation" title="The Aerospace Corporation">The Aerospace Corporation</a> (10 July 2007)</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/DoD/DoD-PUBLICATIONS/DOD_3235x1-H_15048/">DoD 3235.1-H (3rd Ed)</a> <i>Test and Evaluation of System Reliability, Availability, and Maintainability (A Primer)</i>, U.S. Department of Defense (March 1982).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/NASA/NASA-GSFC/GSFC-Code-Series/GSFC_431_REF_000370_2297/">NASA GSFC 431-REF-000370</a> <i>Flight Assurance Procedure: Performing a Failure Mode and Effects Analysis</i>, <a href="/wiki/National_Aeronautics_and_Space_Administration" class="mw-redirect" title="National Aeronautics and Space Administration">National Aeronautics and Space Administration</a> <a href="/wiki/Goddard_Space_Flight_Center" title="Goddard Space Flight Center">Goddard Space Flight Center</a> (10 August 1996).</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220814101207/https://standards.ieee.org/ieee/1332/2026/">IEEE 1332–1998</a> <i>IEEE Standard Reliability Program for the Development and Production of Electronic Systems and Equipment</i>, <a href="/wiki/Institute_of_Electrical_and_Electronics_Engineers" title="Institute of Electrical and Electronics Engineers">Institute of Electrical and Electronics Engineers</a> (1998).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/NASA/NASA-JPL/JPL_D-5703_JUL1990_15049/">JPL D-5703</a> <i>Reliability Analysis Handbook</i>, <a href="/wiki/National_Aeronautics_and_Space_Administration" class="mw-redirect" title="National Aeronautics and Space Administration">National Aeronautics and Space Administration</a> <a href="/wiki/Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a> (July 1990).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-STD/MIL-STD-0700-0799/MIL-STD-785B_23780/">MIL-STD-785B</a> <i>Reliability Program for Systems and Equipment Development and Production</i>, U.S. Department of Defense (15 September 1980). (*Obsolete, superseded by ANSI/GEIA-STD-0009-2008 titled <i>Reliability Program Standard for Systems Design, Development, and Manufacturing</i>, 13 Nov 2008)</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-HDBK/MIL-HDBK-0200-0299/MIL-HDBK-217F_14591/">MIL-HDBK-217F</a> <i>Reliability Prediction of Electronic Equipment</i>, U.S. Department of Defense (2 December 1991).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-HDBK/MIL-HDBK-0200-0299/MIL-HDBK-217F_NOTICE-1_14589/">MIL-HDBK-217F (Notice 1)</a> <i>Reliability Prediction of Electronic Equipment</i>, U.S. Department of Defense (10 July 1992).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-HDBK/MIL-HDBK-0200-0299/MIL-HDBK-217F_NOTICE-2_14590/">MIL-HDBK-217F (Notice 2)</a> <i>Reliability Prediction of Electronic Equipment</i>, U.S. Department of Defense (28 February 1995).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-STD/MIL-STD-0500-0699/MIL-STD-690D_15050/">MIL-STD-690D</a> <i>Failure Rate Sampling Plans and Procedures</i>, U.S. Department of Defense (10 June 2005).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-HDBK/MIL-HDBK-0300-0499/MIL-HDBK-338B_15041/">MIL-HDBK-338B</a> <i>Electronic Reliability Design Handbook</i>, U.S. Department of Defense (1 October 1998).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-HDBK/MIL-HDBK-2000-2999/MIL-HDBK-2173_15046/">MIL-HDBK-2173</a> <i>Reliability-Centered Maintenance (RCM) Requirements for Naval Aircraft, Weapon Systems, and Support Equipment</i>, U.S. Department of Defense (30 January 1998); (superseded by <a rel="nofollow" class="external text" href="http://www.barringer1.com/mil_files/NAVAIR-00-25-403.pdf">NAVAIR 00-25-403</a>).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-STD/MIL-STD-1500-1599/MIL_STD_1543B_166/">MIL-STD-1543B</a> <i>Reliability Program Requirements for Space and Launch Vehicles</i>, U.S. Department of Defense (25 October 1988).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-STD/MIL-STD-1600-1699/MIL_STD_1629A_1556/">MIL-STD-1629A</a> <i>Procedures for Performing a Failure Mode Effects and Criticality Analysis</i>, U.S. Department of Defense (24 November 1980).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/MIL-HDBK/MIL-HDBK-0700-0799/MIL_HDBK_781A_1933/">MIL-HDBK-781A</a> <i>Reliability Test Methods, Plans, and Environments for Engineering Development, Qualification, and Production</i>, U.S. Department of Defense (1 April 1996).</li> <li><a rel="nofollow" class="external text" href="http://www.everyspec.com/USN/NSWC/NSWC-06_RELIAB_HDBK_2006_15051/">NSWC-06 (Part A & B)</a> <i>Handbook of Reliability Prediction Procedures for Mechanical Equipment</i>, <a href="/wiki/Naval_Surface_Warfare_Center" title="Naval Surface Warfare Center">Naval Surface Warfare Center</a> (10 January 2006).</li> <li><a rel="nofollow" class="external text" href="https://telecom-info.njdepot.ericsson.net/site-cgi/ido/docs.cgi?ID=073944231SEARCH&KEYWORDS=&TITLE=&DOCUMENT=sr-332&DATE=&CLASS=&COUNT=1000">SR-332</a> <i>Reliability Prediction Procedure for Electronic Equipment</i>, <a href="/wiki/Telcordia_Technologies" class="mw-redirect" title="Telcordia Technologies">Telcordia Technologies</a> (January 2011).</li> <li><a rel="nofollow" class="external text" href="https://telecom-info.njdepot.ericsson.net/site-cgi/ido/docs.cgi?ID=073944231SEARCH&KEYWORDS=&TITLE=&DOCUMENT=fd-arpp-01&DATE=&CLASS=&COUNT=1000">FD-ARPP-01</a> <i>Automated Reliability Prediction Procedure</i>, <a href="/wiki/Telcordia_Technologies" class="mw-redirect" title="Telcordia Technologies">Telcordia Technologies</a> (January 2011).</li> <li><a rel="nofollow" class="external text" href="https://telecom-info.njdepot.ericsson.net/site-cgi/ido/docs.cgi?DOCUMENT=gr-357&KEYWORDS=&TITLE=&ID=259205889SEARCH">GR-357</a> <i>Generic Requirements for Assuring the Reliability of Components Used in Telecommunications Equipment</i>, <a href="/wiki/Telcordia_Technologies" class="mw-redirect" title="Telcordia Technologies">Telcordia Technologies</a> (March 2001).</li></ul> <p><a rel="nofollow" class="external free" href="http://standards.sae.org/ja1000/1_199903/">http://standards.sae.org/ja1000/1_199903/</a> SAE JA1000/1 Reliability Program Standard Implementation Guide </p> <div class="mw-heading mw-heading3"><h3 id="UK_standards">UK standards</h3></div> <p>In the UK, there are more up to date standards maintained under the sponsorship of UK MOD as Defence Standards. The relevant Standards include: </p><p>DEF STAN 00-40 Reliability and Maintainability (R&M) </p> <ul><li>PART 1: Issue 5: Management Responsibilities and Requirements for Programmes and Plans</li> <li>PART 4: (ARMP-4)Issue 2: Guidance for Writing NATO R&M Requirements Documents</li> <li>PART 6: Issue 1: IN-SERVICE R & M</li> <li>PART 7 (ARMP-7) Issue 1: NATO R&M Terminology Applicable to ARMP's</li></ul> <p>DEF STAN 00-42 RELIABILITY AND MAINTAINABILITY ASSURANCE GUIDES </p> <ul><li>PART 1: Issue 1: ONE-SHOT DEVICES/SYSTEMS</li> <li>PART 2: Issue 1: SOFTWARE</li> <li>PART 3: Issue 2: R&M CASE</li> <li>PART 4: Issue 1: Testability</li> <li>PART 5: Issue 1: IN-SERVICE RELIABILITY DEMONSTRATIONS</li></ul> <p>DEF STAN 00-43 RELIABILITY AND MAINTAINABILITY ASSURANCE ACTIVITY </p> <ul><li>PART 2: Issue 1: IN-SERVICE MAINTAINABILITY DEMONSTRATIONS</li></ul> <p>DEF STAN 00-44 RELIABILITY AND MAINTAINABILITY DATA COLLECTION AND CLASSIFICATION </p> <ul><li>PART 1: Issue 2: MAINTENANCE DATA & DEFECT REPORTING IN THE ROYAL NAVY, THE ARMY AND THE ROYAL AIR FORCE</li> <li>PART 2: Issue 1: DATA CLASSIFICATION AND INCIDENT SENTENCING—GENERAL</li> <li>PART 3: Issue 1: INCIDENT SENTENCING—SEA</li> <li>PART 4: Issue 1: INCIDENT SENTENCING—LAND</li></ul> <p>DEF STAN 00-45 Issue 1: RELIABILITY CENTERED MAINTENANCE </p><p>DEF STAN 00-49 Issue 1: RELIABILITY AND MAINTAINABILITY MOD GUIDE TO TERMINOLOGY DEFINITIONS </p><p>These can be obtained from <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060106062624/http://www.dstan.mod.uk/">DSTAN</a>. There are also many commercial standards, produced by many organisations including the SAE, MSG, ARP, and IEE. </p> <div class="mw-heading mw-heading3"><h3 id="French_standards">French standards</h3></div> <ul><li>FIDES <a rel="nofollow" class="external autonumber" href="http://fides-reliability.org">[1]</a>. The FIDES methodology (UTE-C 80-811) is based on the physics of failures and supported by the analysis of test data, field returns and existing modelling.</li> <li>UTE-C 80–810 or RDF2000 <a rel="nofollow" class="external autonumber" href="http://www.ute-fr.com/FR/">[2]</a>. The RDF2000 methodology is based on the French telecom experience.</li></ul> <div class="mw-heading mw-heading3"><h3 id="International_standards">International standards</h3></div> <ul><li><a rel="nofollow" class="external text" href="http://tc56.iec.ch/about/standards0_1.htm">TC 56 Standards: Dependability</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Reliability_engineering" class="extiw" title="commons:Category:Reliability engineering">Reliability engineering</a> at Wikimedia Commons</li> <li><a rel="nofollow" class="external text" href="http://libarchstor.uah.edu:8081/repositories/2/resources/66">John P. Rankin Collection, The University of Alabama in Huntsville Archives and Special Collections</a> NASA reliability engineering research on sneak circuits.</li> <li><a rel="nofollow" class="external text" href="https://medium.com/@erangadarora/cracking-the-weibull-code-understanding-failure-patterns-with-easy-intution-e0c64dec7a42">Simplifying Hardware Reliability : Intuitive Insights into the Weibull Distribution in less than 5 min ! ..(with Python Code)</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl 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a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Systems_engineering" title="Template:Systems engineering"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Systems_engineering" title="Template talk:Systems engineering"><abbr title="Discuss this template">t</abbr></a></li><li 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management">Configuration management</a></li> <li><a href="/wiki/Earth_systems_engineering_and_management" title="Earth systems engineering and management">Earth systems engineering and management</a></li> <li><a href="/wiki/Electrical_engineering" title="Electrical engineering">Electrical engineering</a></li> <li><a href="/wiki/Enterprise_systems_engineering" title="Enterprise systems engineering">Enterprise systems engineering</a></li> <li><a href="/wiki/Health_systems_engineering" title="Health systems engineering">Health systems engineering</a></li> <li><a href="/wiki/Performance_engineering" title="Performance engineering">Performance engineering</a></li> <li><a class="mw-selflink selflink">Reliability engineering</a></li> <li><a href="/wiki/Safety_engineering" title="Safety engineering">Safety engineering</a></li> <li><a href="/wiki/Stanford_torus" title="Stanford torus">Sociocultural Systems Engineering</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Processes</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Requirements_engineering" title="Requirements engineering">Requirements engineering</a></li> <li><a href="/wiki/Functional_specification" title="Functional specification">Functional specification</a></li> <li><a href="/wiki/System_integration" title="System integration">System integration</a></li> <li><a href="/wiki/Verification_and_validation" title="Verification and validation">Verification and validation</a></li> <li><a href="/wiki/Design_review" title="Design review">Design review</a></li> <li><a href="/wiki/System_of_systems_engineering" title="System of systems engineering">System of systems engineering</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Business_process" title="Business process">Business process</a></li> <li><a href="/wiki/Fault_tolerance" title="Fault tolerance">Fault tolerance</a></li> <li><a href="/wiki/System" title="System">System</a></li> <li><a href="/wiki/System_lifecycle" class="mw-redirect" title="System lifecycle">System lifecycle</a></li> <li><a href="/wiki/V-model" title="V-model">V-Model</a></li> <li><a href="/wiki/Systems_development_life_cycle" title="Systems development life cycle">Systems development life cycle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Tools</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Decision-making" title="Decision-making">Decision-making</a></li> <li><a href="/wiki/Function_model" title="Function model">Function modelling</a></li> <li><a href="/wiki/IDEF" title="IDEF">IDEF</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Optimization</a></li> <li><a href="/wiki/Quality_function_deployment" title="Quality function deployment">Quality function deployment</a></li> <li><a href="/wiki/System_dynamics" title="System dynamics">System dynamics</a></li> <li><a href="/wiki/Systems_Modeling_Language" class="mw-redirect" title="Systems Modeling Language">Systems Modeling Language</a></li> <li><a href="/wiki/Systems_analysis" title="Systems analysis">Systems analysis</a></li> <li><a href="/wiki/Systems_modeling" title="Systems modeling">Systems modeling</a></li> <li><a href="/wiki/Work_breakdown_structure" title="Work breakdown structure">Work breakdown structure</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/James_S._Albus" title="James S. Albus">James S. Albus</a></li> <li><a href="/wiki/Ruzena_Bajcsy" title="Ruzena Bajcsy">Ruzena Bajcsy</a></li> <li><a href="/wiki/Benjamin_S._Blanchard" title="Benjamin S. Blanchard">Benjamin S. Blanchard</a></li> <li><a href="/wiki/Wernher_von_Braun" title="Wernher von Braun">Wernher von Braun</a></li> <li><a href="/wiki/Kathleen_Carley" title="Kathleen Carley">Kathleen Carley</a></li> <li><a href="/wiki/Harold_Chestnut" title="Harold Chestnut">Harold Chestnut</a></li> <li><a href="/wiki/Wolt_Fabrycky" title="Wolt Fabrycky">Wolt Fabrycky</a></li> <li><a href="/wiki/Barbara_Grosz" class="mw-redirect" title="Barbara Grosz">Barbara Grosz</a></li> <li><a href="/wiki/Arthur_David_Hall_III" title="Arthur David Hall III">Arthur David Hall III</a></li> <li><a href="/wiki/Derek_Hitchins" title="Derek Hitchins">Derek Hitchins</a></li> <li><a href="/wiki/Robert_E._Machol" title="Robert E. Machol">Robert E. Machol</a></li> <li><a href="/wiki/Radhika_Nagpal" title="Radhika Nagpal">Radhika Nagpal</a></li> <li><a href="/wiki/Simon_Ramo" title="Simon Ramo">Simon Ramo</a></li> <li><a href="/wiki/Joseph_Francis_Shea" title="Joseph Francis Shea">Joseph Francis Shea</a></li> <li><a href="/wiki/Katia_Sycara" title="Katia Sycara">Katia Sycara</a></li> <li><a href="/wiki/Manuela_M._Veloso" title="Manuela M. Veloso">Manuela M. Veloso</a></li> <li><a href="/wiki/John_N._Warfield" title="John N. Warfield">John N. Warfield</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related fields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Control_engineering" title="Control engineering">Control engineering</a></li> <li><a href="/wiki/Computer_engineering" title="Computer engineering">Computer engineering</a></li> <li><a href="/wiki/Industrial_engineering" title="Industrial engineering">Industrial engineering</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li> <li><a href="/wiki/Project_management" title="Project management">Project management</a></li> <li><a href="/wiki/Quality_management" title="Quality management">Quality management</a></li> <li><a href="/wiki/Risk_management" title="Risk management">Risk management</a></li> <li><a href="/wiki/Software_engineering" title="Software engineering">Software engineering</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Category:Systems_engineering" title="Category:Systems engineering">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Software_engineering" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Software_engineering" title="Template:Software engineering"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Software_engineering" title="Template talk:Software engineering"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Software_engineering" title="Special:EditPage/Template:Software engineering"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Software_engineering" style="font-size:114%;margin:0 4em"><a href="/wiki/Software_engineering" title="Software engineering">Software engineering</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_programming" title="Computer programming">Computer programming</a></li> <li><a href="/wiki/DevOps" title="DevOps">DevOps</a></li> <li><a href="/wiki/Empirical_software_engineering" title="Empirical software engineering">Empirical software engineering</a></li> <li><a href="/wiki/Experimental_software_engineering" title="Experimental software engineering">Experimental software engineering</a></li> <li><a href="/wiki/Formal_methods" title="Formal methods">Formal methods</a></li> <li><a href="/wiki/Requirements_engineering" title="Requirements engineering">Requirements engineering</a></li> <li><a href="/wiki/Search-based_software_engineering" title="Search-based software engineering">Search-based software engineering</a></li> <li><a href="/wiki/Site_reliability_engineering" title="Site reliability engineering">Site reliability engineering</a></li> <li><a href="/wiki/Social_software_engineering" title="Social software engineering">Social software engineering</a></li> <li><a href="/wiki/Software_deployment" title="Software deployment">Software deployment</a></li> <li><a href="/wiki/Software_design" title="Software design">Software design</a></li> <li><a href="/wiki/Software_maintenance" title="Software maintenance">Software maintenance</a></li> <li><a href="/wiki/Software_testing" title="Software testing">Software testing</a></li> <li><a href="/wiki/Systems_analysis" title="Systems analysis">Systems analysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abstraction_(computer_science)" title="Abstraction (computer science)">Abstraction</a></li> <li><a href="/wiki/Component-based_software_engineering" title="Component-based software engineering">Component-based software engineering</a></li> <li><a href="/wiki/Computer_compatibility" title="Computer compatibility">Software compatibility</a> <ul><li><a href="/wiki/Backward_compatibility" title="Backward compatibility">Backward compatibility</a></li> <li><a href="/wiki/Compatibility_layer" title="Compatibility layer">Compatibility layer</a></li> <li><a href="/wiki/Compatibility_mode" title="Compatibility mode">Compatibility mode</a></li> <li><a href="/wiki/Forward_compatibility" title="Forward compatibility">Forward compatibility</a></li> <li><a href="/wiki/Software_incompatibility" title="Software incompatibility">Software incompatibility</a></li></ul></li> <li><a href="/wiki/Data_modeling" title="Data modeling">Data modeling</a></li> <li><a href="/wiki/Enterprise_architecture" title="Enterprise architecture">Enterprise architecture</a></li> <li><a href="/wiki/Functional_specification" title="Functional specification">Functional specification</a></li> <li><a href="/wiki/Modeling_language" title="Modeling language">Modeling language</a></li> <li><a href="/wiki/Programming_paradigm" title="Programming paradigm">Programming paradigm</a></li> <li><a href="/wiki/Software" title="Software">Software</a></li> <li><a href="/wiki/Software_archaeology" title="Software archaeology">Software archaeology</a></li> <li><a href="/wiki/Software_architecture" title="Software architecture">Software architecture</a></li> <li><a href="/wiki/Software_configuration_management" title="Software configuration management">Software configuration management</a></li> <li><a href="/wiki/Software_development_process" title="Software development process">Software development process/methodology</a></li> <li><a href="/wiki/Software_quality" title="Software quality">Software quality</a></li> <li><a href="/wiki/Software_quality_assurance" title="Software quality assurance">Software quality assurance</a></li> <li><a href="/wiki/Software_verification_and_validation" title="Software verification and validation">Software verification and validation</a></li> <li><a href="/wiki/Software_system" title="Software system">Software system</a></li> <li><a href="/wiki/Structured_analysis" title="Structured analysis">Structured analysis</a> <ul><li><a href="/wiki/Essential_systems_analysis" title="Essential systems analysis">Essential analysis</a></li></ul></li> <li><a href="/wiki/CI/CD" title="CI/CD">CI/CD</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Orientations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Agile_software_development" title="Agile software development">Agile</a></li> <li><a href="/wiki/Aspect-oriented_programming" title="Aspect-oriented programming">Aspect-oriented</a></li> <li><a href="/wiki/Object-oriented_programming" title="Object-oriented programming">Object orientation</a></li> <li><a href="/wiki/Ontology_(information_science)" title="Ontology (information science)">Ontology</a></li> <li><a href="/wiki/Service-oriented_architecture" title="Service-oriented architecture">Service orientation</a></li> <li><a href="/wiki/Systems_development_life_cycle" title="Systems development life cycle">SDLC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Models</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Developmental</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Agile_software_development" title="Agile software development">Agile</a></li> <li><a href="/wiki/Enterprise_unified_process" title="Enterprise unified process">EUP</a></li> <li><a href="/wiki/Executable_UML" title="Executable UML">Executable UML</a></li> <li><a href="/wiki/Incremental_build_model" title="Incremental build model">Incremental model</a></li> <li><a href="/wiki/Iterative_and_incremental_development" title="Iterative and incremental development">Iterative model</a></li> <li><a href="/wiki/Software_prototyping" title="Software prototyping">Prototype model</a></li> <li><a href="/wiki/Rapid_application_development" title="Rapid application development">RAD</a></li> <li><a href="/wiki/Unified_Process" class="mw-redirect" title="Unified Process">UP</a></li> <li><a href="/wiki/Scrum_(software_development)" title="Scrum (software development)">Scrum</a></li> <li><a href="/wiki/Spiral_model" title="Spiral model">Spiral model</a></li> <li><a href="/wiki/V-model_(software_development)" title="V-model (software development)">V-model</a></li> <li><a href="/wiki/Waterfall_model" title="Waterfall model">Waterfall model</a></li> <li><a href="/wiki/Extreme_programming" title="Extreme programming">XP</a></li> <li><a href="/wiki/Model-driven_engineering" title="Model-driven engineering">Model-driven engineering</a></li> <li><a href="/wiki/Round-trip_engineering" title="Round-trip engineering">Round-trip engineering</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ISO/IEC_15504" title="ISO/IEC 15504">SPICE</a></li> <li><a href="/wiki/Capability_Maturity_Model_Integration" title="Capability Maturity Model Integration">CMMI</a></li> <li><a href="/wiki/Data_model" title="Data model">Data model</a></li> <li><a href="/wiki/Entity%E2%80%93relationship_model" title="Entity–relationship model">ER model</a></li> <li><a href="/wiki/Function_model" title="Function model">Function model</a></li> <li><a href="/wiki/Information_model" title="Information model">Information model</a></li> <li><a href="/wiki/Metamodeling" title="Metamodeling">Metamodeling</a></li> <li><a href="/wiki/Object_model" title="Object model">Object model</a></li> <li><a href="/wiki/Systems_modeling" title="Systems modeling">Systems model</a></li> <li><a href="/wiki/View_model" title="View model">View model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Languages</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/IDEF" title="IDEF">IDEF</a></li> <li><a href="/wiki/Unified_Modeling_Language" title="Unified Modeling Language">UML</a></li> <li><a href="/wiki/Universal_Systems_Language" title="Universal Systems Language">USL</a></li> <li><a href="/wiki/Systems_modeling_language" title="Systems modeling language">SysML</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related fields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_science" title="Computer science">Computer science</a></li> <li><a href="/wiki/Computer_engineering" title="Computer engineering">Computer engineering</a></li> <li><a href="/wiki/Information_science" title="Information science">Information science</a></li> <li><a href="/wiki/Project_management" title="Project management">Project management</a></li> <li><a href="/wiki/Risk_management" title="Risk management">Risk management</a></li> <li><a href="/wiki/Systems_engineering" title="Systems engineering">Systems engineering</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="font-weight:bold;"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" 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href="/wiki/Category:Software_engineering" title="Category:Software engineering">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Software_quality" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Software_quality" title="Template:Software quality"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Software_quality" title="Template talk:Software quality"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Software_quality" title="Special:EditPage/Template:Software quality"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Software_quality" style="font-size:114%;margin:0 4em"><a href="/wiki/Software_quality" title="Software quality">Software quality</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Qualities</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Internal</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Software_sizing" title="Software sizing">Size</a></li> <li><a href="/wiki/Maintainability#Software_engineering" title="Maintainability">Maintainability</a></li> <li><a href="/wiki/Flexibility_(engineering)" title="Flexibility (engineering)">Flexibility</a></li> <li><a href="/wiki/Software_portability" title="Software portability">Portability</a></li> <li><a href="/wiki/Reusability" title="Reusability">Reusability</a></li> <li><a href="/wiki/Computer_programming#Readability_of_source_code" title="Computer programming">Readability</a></li> <li><a href="/wiki/Scalability" title="Scalability">Scalability</a></li> <li><a href="/wiki/Software_testability" title="Software testability">Testability</a></li> <li><a href="/wiki/Understandability" class="mw-redirect" title="Understandability">Understandability</a></li> <li><a href="/wiki/Loose_coupling" title="Loose coupling">Loose coupling</a></li> <li><a href="/wiki/Orthogonality_(programming)" title="Orthogonality (programming)">Orthogonality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">External</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Usability" title="Usability">Usability</a></li> <li><a class="mw-selflink selflink">Reliability</a></li> <li><a href="/wiki/Adaptability" title="Adaptability">Adaptability</a></li> <li><a href="/wiki/Correctness_(computer_science)" title="Correctness (computer science)">Correctness</a></li> <li><a href="/wiki/Accuracy_and_precision" title="Accuracy and precision">Accuracy</a></li> <li><a href="/wiki/Algorithmic_efficiency" title="Algorithmic efficiency">Efficiency</a></li> <li><a href="/wiki/Robustness_(computer_science)" title="Robustness (computer science)">Robustness</a></li> <li><a href="/wiki/Software_development_security" class="mw-redirect" title="Software development security">Security</a></li> <li><a href="/wiki/Software_system_safety" class="mw-redirect" title="Software system safety">Safety</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Standards and lists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ISO/IEC_9126" title="ISO/IEC 9126">ISO/IEC 9126</a></li> <li><a href="/wiki/Non-functional_requirement#Examples" title="Non-functional requirement">Non-functional requirements</a></li> <li><a href="/wiki/List_of_system_quality_attributes" title="List of system quality attributes">List of system quality attributes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Processes</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Software_quality_management" title="Software quality management">Software quality management</a></li> <li><a href="/wiki/Software_quality_control" title="Software quality control">Software quality control</a></li> <li><a href="/wiki/Software_quality_assurance" title="Software quality assurance">Software quality assurance</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="font-weight:bold;"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Software_quality" class="extiw" title="commons:Category:Software quality">Commons</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Engineering" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Engineering_fields" title="Template:Engineering fields"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Engineering_fields" title="Template talk:Engineering fields"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Engineering_fields" title="Special:EditPage/Template:Engineering fields"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Engineering" style="font-size:114%;margin:0 4em"><a href="/wiki/Engineering" title="Engineering">Engineering</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><a href="/wiki/History_of_engineering" title="History of engineering">History</a></li> <li><a href="/wiki/Outline_of_engineering" title="Outline of engineering">Outline</a></li> <li><a href="/wiki/List_of_engineering_branches" title="List of engineering branches">List of engineering branches</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Specialties<br />and<br /><a href="/wiki/Interdisciplinarity" title="Interdisciplinarity">Interdisciplinarity</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Civil_engineering" title="Civil engineering">Civil</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Architectural_engineering" title="Architectural engineering">Architectural</a></li> <li><a href="/wiki/Coastal_engineering" title="Coastal engineering">Coastal</a></li> <li><a href="/wiki/Construction_engineering" title="Construction engineering">Construction</a></li> <li><a href="/wiki/Earthquake_engineering" title="Earthquake engineering">Earthquake</a></li> <li><a href="/wiki/Ecological_engineering" title="Ecological engineering">Ecological</a></li> <li><a href="/wiki/Environmental_engineering" title="Environmental engineering">Environmental</a> <ul><li><a href="/wiki/Sanitary_engineering" title="Sanitary engineering">Sanitary</a></li></ul></li> <li><a href="/wiki/Geological_engineering" title="Geological engineering">Geological</a></li> <li><a href="/wiki/Geotechnical_engineering" title="Geotechnical engineering">Geotechnical</a></li> <li><a href="/wiki/Hydraulic_engineering" title="Hydraulic engineering">Hydraulic</a></li> <li><a href="/wiki/Mining_engineering" title="Mining engineering">Mining</a></li> <li><a href="/wiki/Municipal_or_urban_engineering" title="Municipal or urban engineering">Municipal/Urban</a></li> <li><a href="/wiki/Offshore_engineering" class="mw-redirect" title="Offshore engineering">Offshore</a></li> <li><a href="/wiki/River_engineering" title="River engineering">River</a></li> <li><a href="/wiki/Structural_engineering" title="Structural engineering">Structural</a></li> <li><a href="/wiki/Transportation_engineering" title="Transportation engineering">Transportation</a> <ul><li><a href="/wiki/Traffic_engineering_(transportation)" title="Traffic engineering (transportation)">Traffic</a></li> <li><a href="/wiki/Railway_engineering" title="Railway engineering">Railway</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mechanical_engineering" title="Mechanical engineering">Mechanical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acoustical_engineering" title="Acoustical engineering">Acoustic</a></li> <li><a href="/wiki/Aerospace_engineering" title="Aerospace engineering">Aerospace</a></li> <li><a href="/wiki/Automotive_engineering" title="Automotive engineering">Automotive</a></li> <li><a href="/wiki/Biomechanical_engineering" title="Biomechanical engineering">Biomechanical</a></li> <li><a href="/wiki/Energy_engineering" title="Energy engineering">Energy</a></li> <li><a href="/wiki/Manufacturing_engineering" title="Manufacturing engineering">Manufacturing</a></li> <li><a href="/wiki/Marine_engineering" title="Marine engineering">Marine</a></li> <li><a href="/wiki/Naval_architecture" title="Naval architecture">Naval architecture</a></li> <li><a href="/wiki/Railway_engineering" title="Railway engineering">Railway</a></li> <li><a href="/wiki/Sports_engineering" title="Sports engineering">Sports</a></li> <li><a href="/wiki/Thermal_engineering" title="Thermal engineering">Thermal</a></li> <li><a href="/wiki/Tribology" title="Tribology">Tribology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Electrical_engineering" title="Electrical engineering">Electrical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Broadcast_engineering" title="Broadcast engineering">Broadcast</a> <ul><li><a href="/wiki/Outline_of_computer_engineering" title="Outline of computer engineering">outline</a></li></ul></li> <li><a href="/wiki/Control_engineering" title="Control engineering">Control</a></li> <li><a href="/wiki/Electromechanics" title="Electromechanics">Electromechanics</a></li> <li><a href="/wiki/Electronic_engineering" title="Electronic engineering">Electronics</a></li> <li><a href="/wiki/Microwave_engineering" title="Microwave engineering">Microwaves</a></li> <li><a href="/wiki/Optical_engineering" title="Optical engineering">Optical</a></li> <li><a href="/wiki/Power_engineering" title="Power engineering">Power</a></li> <li><a href="/wiki/Radio-frequency_engineering" title="Radio-frequency engineering">Radio frequency</a></li> <li><a href="/wiki/Signal_processing" title="Signal processing">Signal processing</a></li> <li><a href="/wiki/Telecommunications_engineering" title="Telecommunications engineering">Telecommunications</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chemical_engineering" title="Chemical engineering">Chemical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biochemical_engineering" title="Biochemical engineering">Biochemical/Bioprocess</a></li> <li><a href="/wiki/Biological_engineering" title="Biological engineering">Biological</a> <ul><li><a href="/wiki/Bioresource_engineering" title="Bioresource engineering">Bioresource</a></li> <li><a href="/wiki/Genetic_engineering" title="Genetic engineering">Genetic</a></li> <li><a href="/wiki/Tissue_engineering" title="Tissue engineering">Tissue</a></li></ul></li> <li><a href="/wiki/Chemical_reaction_engineering" title="Chemical reaction engineering">Chemical reaction</a></li> <li><a href="/wiki/Electrochemical_engineering" title="Electrochemical engineering">Electrochemical</a></li> <li><a href="/wiki/Food_engineering" title="Food engineering">Food</a></li> <li><a href="/wiki/Molecular_engineering" title="Molecular engineering">Molecular</a></li> <li><a href="/wiki/Paper_engineering" title="Paper engineering">Paper</a></li> <li><a href="/wiki/Petroleum_engineering" title="Petroleum engineering">Petroleum</a></li> <li><a href="/wiki/Process_engineering" title="Process engineering">Process</a></li> <li><a href="/wiki/Chemical_reaction_engineering" title="Chemical reaction engineering">Reaction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Materials_science" title="Materials science">Materials</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biomaterial" title="Biomaterial">Biomaterial</a></li> <li><a href="/wiki/Ceramic_engineering" title="Ceramic engineering">Ceramics</a></li> <li><a href="/wiki/Corrosion_engineering" title="Corrosion engineering">Corrosion</a></li> <li><a href="/wiki/Metallurgy" title="Metallurgy">Metallurgy</a></li> <li><a href="/wiki/Molecular_engineering" title="Molecular engineering">Molecular</a></li> <li><a href="/wiki/Nanotechnology" title="Nanotechnology">Nanotechnology</a></li> <li><a href="/wiki/Polymer_engineering" title="Polymer engineering">Polymers</a></li> <li><a href="/wiki/Semiconductor_device" title="Semiconductor device">Semiconductors</a></li> <li><a href="/wiki/Surface_engineering" title="Surface engineering">Surfaces</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_engineering" title="Computer engineering">Computer</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Artificial_intelligence_engineering" title="Artificial intelligence engineering">AI</a></li> <li><a href="/wiki/Computer_engineering" title="Computer engineering">Computer</a></li> <li><a href="/wiki/Cybersecurity_engineering" title="Cybersecurity engineering">Cybersecurity</a></li> <li><a href="/wiki/Data_engineering" title="Data engineering">Data</a></li> <li><a href="/wiki/Computer_network_engineering" title="Computer network engineering">Networks</a></li> <li><a href="/wiki/Robotics_engineering" title="Robotics engineering">Robotics</a></li> <li><a href="/wiki/Software_engineering" title="Software engineering">Software</a></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_kcmsystem.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Nuvola_apps_kcmsystem.png/50px-Nuvola_apps_kcmsystem.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Nuvola_apps_kcmsystem.png/75px-Nuvola_apps_kcmsystem.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Nuvola_apps_kcmsystem.png/100px-Nuvola_apps_kcmsystem.png 2x" data-file-width="128" data-file-height="128" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Engineering_education" title="Engineering education">Engineering education</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bachelor_of_Engineering" title="Bachelor of Engineering">Bachelor of Engineering</a></li> <li><a href="/wiki/Bachelor_of_Science" title="Bachelor of Science">Bachelor of Science</a></li> <li><a href="/wiki/Master%27s_degree" title="Master's degree">Master's degree</a></li> <li><a href="/wiki/Doctorate" title="Doctorate">Doctorate</a></li> <li><a href="/wiki/Graduate_certificate" title="Graduate certificate">Graduate certificate</a></li> <li><a href="/wiki/Engineer%27s_degree" title="Engineer's degree">Engineer's degree</a></li> <li><a href="/wiki/Regulation_and_licensure_in_engineering" title="Regulation and licensure in engineering">Licensed engineer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Engineer" title="Engineer">Engineer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Glossary" title="Glossary">Glossaries</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Engineering <ul><li><a href="/wiki/Glossary_of_engineering:_A%E2%80%93L" title="Glossary of engineering: A–L">A–L</a></li> <li><a href="/wiki/Glossary_of_engineering:_M%E2%80%93Z" title="Glossary of engineering: M–Z">M–Z</a></li></ul></li> <li><a href="/wiki/Glossary_of_aerospace_engineering" title="Glossary of aerospace engineering">Aerospace engineering</a></li> <li><a href="/wiki/Glossary_of_civil_engineering" title="Glossary of civil engineering">Civil engineering</a></li> <li><a href="/wiki/Glossary_of_electrical_and_electronics_engineering" title="Glossary of electrical and electronics engineering">Electrical and electronics engineering</a></li> <li><a href="/wiki/Glossary_of_mechanical_engineering" title="Glossary of mechanical engineering">Mechanical engineering</a></li> <li><a href="/wiki/Glossary_of_structural_engineering" title="Glossary of structural engineering">Structural engineering</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Agricultural_engineering" title="Agricultural engineering">Agricultural</a></li> <li><a href="/wiki/Audio_engineer" title="Audio engineer">Audio</a></li> <li><a href="/wiki/Automation_engineering" title="Automation engineering">Automation</a></li> <li><a href="/wiki/Biomedical_engineering" title="Biomedical engineering">Biomedical</a> <ul><li><a href="/wiki/Bioinformatics" title="Bioinformatics">Bioinformatics</a></li> <li><a href="/wiki/Clinical_engineering" title="Clinical engineering">Clinical</a></li> <li><a href="/wiki/Health_technology" title="Health technology">Health technology</a></li> <li><a href="/wiki/Pharmaceutical_engineering" title="Pharmaceutical engineering">Pharmaceutical</a></li> <li><a href="/wiki/Rehabilitation_engineering" title="Rehabilitation engineering">Rehabilitation</a></li></ul></li> <li><a href="/wiki/Building_services_engineering" title="Building services engineering">Building services</a> <ul><li><a href="/wiki/Mechanical,_electrical,_and_plumbing" title="Mechanical, electrical, and plumbing">MEP</a></li></ul></li> <li><a href="/wiki/Design_engineer" title="Design engineer">Design</a></li> <li><a href="/wiki/Explosives_engineering" title="Explosives engineering">Explosives</a></li> <li><a href="/wiki/Facilities_engineering" title="Facilities engineering">Facilities</a></li> <li><a href="/wiki/Fire_protection_engineering" title="Fire protection engineering">Fire</a></li> <li><a href="/wiki/Forensic_engineering" title="Forensic engineering">Forensic</a></li> <li><a href="/wiki/Climate_engineering" title="Climate engineering">Climate</a></li> <li><a href="/wiki/Geomatics_engineering" class="mw-redirect" title="Geomatics engineering">Geomatics</a></li> <li><a href="/wiki/Engineering_drawing" title="Engineering drawing">Graphics</a></li> <li><a href="/wiki/Industrial_engineering" title="Industrial engineering">Industrial</a></li> <li><a href="/wiki/Information_engineering" title="Information engineering">Information</a></li> <li><a href="/wiki/Instrumentation_engineering" class="mw-redirect" title="Instrumentation engineering">Instrumentation</a> <ul><li><a href="/wiki/Instrumentation_and_control_engineering" title="Instrumentation and control engineering">and Control</a></li></ul></li> <li><a href="/wiki/Logistics_engineering" title="Logistics engineering">Logistics</a></li> <li><a href="/wiki/Engineering_management" title="Engineering management">Management</a></li> <li><a href="/wiki/Engineering_mathematics" title="Engineering mathematics">Mathematics</a></li> <li><a href="/wiki/Mechatronics" title="Mechatronics">Mechatronics</a></li> <li><a href="/wiki/Military_engineering" title="Military engineering">Military</a></li> <li><a href="/wiki/Nuclear_engineering" title="Nuclear engineering">Nuclear</a></li> <li><a href="/wiki/Ontology_engineering" title="Ontology engineering">Ontology</a></li> <li><a href="/wiki/Packaging_engineering" title="Packaging engineering">Packaging</a></li> <li><a href="/wiki/Engineering_physics" title="Engineering physics">Physics</a></li> <li><a href="/wiki/Privacy_engineering" title="Privacy engineering">Privacy</a></li> <li><a href="/wiki/Safety_engineering" title="Safety engineering">Safety</a></li> <li><a href="/wiki/Security_engineering" title="Security engineering">Security</a></li> <li><a href="/wiki/Survey_engineering" class="mw-redirect" title="Survey engineering">Survey</a></li> <li><a href="/wiki/Sustainable_engineering" title="Sustainable engineering">Sustainability</a></li> <li><a href="/wiki/Systems_engineering" title="Systems engineering">Systems</a></li> <li><a href="/wiki/Textile_engineering" class="mw-redirect" title="Textile engineering">Textile</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3" style="font-weight:bold;"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Engineering" title="Category:Engineering">Category</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <a href="https://commons.wikimedia.org/wiki/Engineering" class="extiw" title="commons:Engineering">Commons</a></li> <li><span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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href="/wiki/Portal:Engineering" title="Portal:Engineering">Portal</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Systems_science" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Systems_science" title="Template:Systems science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Systems_science" title="Template talk:Systems science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Systems_science" title="Special:EditPage/Template:Systems science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Systems_science" style="font-size:114%;margin:0 4em"><a href="/wiki/Systems_science" title="Systems science">Systems science</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/System" title="System">System</a><br />types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Systems_art" title="Systems art">Art</a></li> <li><a href="/wiki/Biological_system" title="Biological system">Biological</a></li> <li><a href="/wiki/Complex_system" title="Complex system">Complex</a></li> <li><a href="/wiki/Coupled_human%E2%80%93environment_system" title="Coupled human–environment system">Coupled human–environment</a></li> <li><a href="/wiki/Ecosystem" title="Ecosystem">Ecological</a></li> <li><a href="/wiki/Economic_system" title="Economic system">Economic</a></li> <li><a href="/wiki/Information_system" title="Information system">Information</a></li> <li><a href="/wiki/Multi-agent_system" title="Multi-agent system">Multi-agent</a></li> <li><a href="/wiki/Nervous_system" title="Nervous system">Nervous</a></li> <li><a href="/wiki/Recommender_system" title="Recommender system">Recommender</a></li> <li><a href="/wiki/Social_system" title="Social system">Social</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Doubling_time" title="Doubling time">Doubling time</a></li> <li><a href="/wiki/Twelve_leverage_points" title="Twelve leverage points">Leverage points</a></li> <li><a href="/wiki/Limiting_factor" title="Limiting factor">Limiting factor</a></li> <li><a href="/wiki/Negative_feedback" title="Negative feedback">Negative feedback</a></li> <li><a href="/wiki/Positive_feedback" title="Positive feedback">Positive feedback</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theoretical<br />fields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Control_theory" title="Control theory">Control theory</a></li> <li><a href="/wiki/Cybernetics" title="Cybernetics">Cybernetics</a></li> <li><a href="/wiki/Earth_system_science" title="Earth system science">Earth system science</a></li> <li><a href="/wiki/Living_systems" title="Living systems">Living systems</a></li> <li><a href="/wiki/Sociotechnical_system" title="Sociotechnical system">Sociotechnical system</a></li> <li><a href="/wiki/Systemics" title="Systemics">Systemics</a></li> <li><a href="/wiki/Urban_metabolism" title="Urban metabolism">Urban metabolism</a></li> <li><a href="/wiki/World-systems_theory" title="World-systems theory">World-systems theory</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Systems_analysis" title="Systems analysis">Analysis</a></li> <li><a href="/wiki/Systems_biology" title="Systems biology">Biology</a></li> <li><a href="/wiki/System_dynamics" title="System dynamics">Dynamics</a></li> <li><a href="/wiki/Systems_ecology" title="Systems ecology">Ecology</a></li> <li><a href="/wiki/Systems_engineering" title="Systems engineering">Engineering</a></li> <li><a href="/wiki/Systems_neuroscience" title="Systems neuroscience">Neuroscience</a></li> <li><a href="/wiki/Systems_pharmacology" title="Systems pharmacology">Pharmacology</a></li> <li><a href="/wiki/Systems_philosophy" title="Systems philosophy">Philosophy</a></li> <li><a href="/wiki/Systems_psychology" title="Systems psychology">Psychology</a></li> <li><a href="/wiki/Systems_theory" title="Systems theory">Theory</a> (<a href="/wiki/Systems_thinking" title="Systems thinking">Systems thinking</a>)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_systems_scientists" title="List of systems scientists">Scientists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Russell_L._Ackoff" title="Russell L. Ackoff">Russell L. Ackoff</a></li> <li><a href="/wiki/Victor_Aladjev" title="Victor Aladjev">Victor Aladjev</a></li> <li><a href="/wiki/William_Ross_Ashby" class="mw-redirect" title="William Ross Ashby">William Ross Ashby</a></li> <li><a href="/wiki/Ruzena_Bajcsy" title="Ruzena Bajcsy">Ruzena Bajcsy</a></li> <li><a href="/wiki/B%C3%A9la_H._B%C3%A1n%C3%A1thy" title="Béla H. Bánáthy">Béla H. Bánáthy</a></li> <li><a href="/wiki/Gregory_Bateson" title="Gregory Bateson">Gregory Bateson</a></li> <li><a href="/wiki/Anthony_Stafford_Beer" class="mw-redirect" title="Anthony Stafford Beer">Anthony Stafford Beer</a></li> <li><a href="/wiki/Richard_E._Bellman" title="Richard E. Bellman">Richard E. Bellman</a></li> <li><a href="/wiki/Ludwig_von_Bertalanffy" title="Ludwig von Bertalanffy">Ludwig von Bertalanffy</a></li> <li><a href="/wiki/Margaret_Boden" title="Margaret Boden">Margaret Boden</a></li> <li><a href="/wiki/Alexander_Bogdanov" title="Alexander Bogdanov">Alexander Bogdanov</a></li> <li><a href="/wiki/Kenneth_E._Boulding" title="Kenneth E. Boulding">Kenneth E. Boulding</a></li> <li><a href="/wiki/Murray_Bowen" title="Murray Bowen">Murray Bowen</a></li> <li><a href="/wiki/Kathleen_Carley" title="Kathleen Carley">Kathleen Carley</a></li> <li><a href="/wiki/Mary_Cartwright" title="Mary Cartwright">Mary Cartwright</a></li> <li><a href="/wiki/C._West_Churchman" title="C. West Churchman">C. West Churchman</a></li> <li><a href="/wiki/Manfred_Clynes" title="Manfred Clynes">Manfred Clynes</a></li> <li><a href="/wiki/George_Dantzig" title="George Dantzig">George Dantzig</a></li> <li><a href="/wiki/Edsger_W._Dijkstra" title="Edsger W. Dijkstra">Edsger W. Dijkstra</a></li> <li><a href="/wiki/Fred_Emery" title="Fred Emery">Fred Emery</a></li> <li><a href="/wiki/Heinz_von_Foerster" title="Heinz von Foerster">Heinz von Foerster</a></li> <li><a href="/wiki/Stephanie_Forrest" title="Stephanie Forrest">Stephanie Forrest</a></li> <li><a href="/wiki/Jay_Wright_Forrester" title="Jay Wright Forrester">Jay Wright Forrester</a></li> <li><a href="/wiki/Barbara_J._Grosz" title="Barbara J. Grosz">Barbara Grosz</a></li> <li><a href="/wiki/Charles_A._S._Hall" title="Charles A. S. Hall">Charles A. S. Hall</a></li> <li><a href="/wiki/Mike_Jackson_(systems_scientist)" title="Mike Jackson (systems scientist)">Mike Jackson</a></li> <li><a href="/wiki/Lydia_Kavraki" title="Lydia Kavraki">Lydia Kavraki</a></li> <li><a href="/wiki/James_J._Kay" title="James J. Kay">James J. Kay</a></li> <li><a href="/wiki/Faina_Mihajlovna_Kirillova" class="mw-redirect" title="Faina Mihajlovna Kirillova">Faina M. Kirillova</a></li> <li><a href="/wiki/George_Klir" title="George Klir">George Klir</a></li> <li><a href="/wiki/Allenna_Leonard" title="Allenna Leonard">Allenna Leonard</a></li> <li><a href="/wiki/Edward_Norton_Lorenz" title="Edward Norton Lorenz">Edward Norton Lorenz</a></li> <li><a href="/wiki/Niklas_Luhmann" title="Niklas Luhmann">Niklas Luhmann</a></li> <li><a href="/wiki/Humberto_Maturana" title="Humberto Maturana">Humberto Maturana</a></li> <li><a href="/wiki/Margaret_Mead" title="Margaret Mead">Margaret Mead</a></li> <li><a href="/wiki/Donella_Meadows" title="Donella Meadows">Donella Meadows</a></li> <li><a href="/wiki/Mihajlo_D._Mesarovic" title="Mihajlo D. Mesarovic">Mihajlo D. Mesarovic</a></li> <li><a href="/wiki/James_Grier_Miller" title="James Grier Miller">James Grier Miller</a></li> <li><a href="/wiki/Radhika_Nagpal" title="Radhika Nagpal">Radhika Nagpal</a></li> <li><a href="/wiki/Howard_T._Odum" title="Howard T. Odum">Howard T. Odum</a></li> <li><a href="/wiki/Talcott_Parsons" title="Talcott Parsons">Talcott Parsons</a></li> <li><a href="/wiki/Ilya_Prigogine" title="Ilya Prigogine">Ilya Prigogine</a></li> <li><a href="/wiki/Qian_Xuesen" title="Qian Xuesen">Qian Xuesen</a></li> <li><a href="/wiki/Anatol_Rapoport" title="Anatol Rapoport">Anatol Rapoport</a></li> <li><a href="/wiki/John_Seddon" title="John Seddon">John Seddon</a></li> <li><a href="/wiki/Peter_Senge" title="Peter Senge">Peter Senge</a></li> <li><a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a></li> <li><a href="/wiki/Katia_Sycara" title="Katia Sycara">Katia Sycara</a></li> <li><a href="/wiki/Eric_Trist" title="Eric Trist">Eric Trist</a></li> <li><a href="/wiki/Francisco_Varela" title="Francisco Varela">Francisco Varela</a></li> <li><a href="/wiki/Manuela_M._Veloso" title="Manuela M. Veloso">Manuela M. Veloso</a></li> <li><a href="/wiki/Kevin_Warwick" title="Kevin Warwick">Kevin Warwick</a></li> <li><a href="/wiki/Norbert_Wiener" title="Norbert Wiener">Norbert Wiener</a></li> <li><a href="/wiki/Jennifer_Wilby" title="Jennifer Wilby">Jennifer Wilby</a></li> <li><a href="/wiki/Anthony_Wilden" title="Anthony Wilden">Anthony Wilden</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Systems_theory_in_anthropology" title="Systems theory in anthropology">Systems theory in anthropology</a></li> <li><a href="/wiki/Systems_theory_in_archaeology" title="Systems theory in archaeology">Systems theory in archaeology</a></li> <li><a href="/wiki/Systems_theory_in_political_science" title="Systems theory in political science">Systems theory in political science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_systems_sciences_organizations" title="List of systems sciences organizations">List</a></li> <li><a href="/wiki/Principia_Cybernetica" title="Principia Cybernetica">Principia Cybernetica</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Systems_science" title="Category:Systems science">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span> <b><a href="/wiki/Portal:Systems_science" title="Portal:Systems science">Portal</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Systems_theory" class="extiw" title="commons:Category:Systems theory">Commons</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1239334494">@media screen{html.skin-theme-clientpref-night .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-night 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navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Design" title="Template:Design"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Design" title="Template talk:Design"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Design" title="Special:EditPage/Template:Design"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Design" style="font-size:114%;margin:0 4em"><a href="/wiki/Design" title="Design">Design</a></div></th></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div> <ul><li><a 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<li><a href="/wiki/News_design" title="News design">News design</a></li> <li><a href="/wiki/Photography" title="Photography">Photography</a></li> <li><a href="/wiki/Retail_design" title="Retail design">Retail design</a></li> <li><a href="/wiki/Signage" title="Signage">Signage</a> / <a href="/wiki/Traffic_sign_design" title="Traffic sign design">Traffic sign design</a></li> <li><a href="/wiki/Typography" title="Typography">Typography</a> / <a href="/wiki/Type_design" title="Type design">Type design</a></li> <li><a href="/wiki/Video_design" title="Video design">Video design</a></li> <li><a href="/wiki/Visual_merchandising" title="Visual merchandising">Visual merchandising</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Environmental_design" title="Environmental design">Environmental<br />design</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Architecture" title="Architecture">Architecture</a></li> <li><a href="/wiki/Architectural_lighting_design" title="Architectural lighting design">Architectural lighting design</a></li> <li><a href="/wiki/Building_design" title="Building design">Building design</a> <ul><li><a href="/wiki/Passive_solar_building_design" title="Passive solar building design">Passive solar</a></li></ul></li> <li><a href="/wiki/Ecological_design" title="Ecological design">Ecological design</a></li> <li><a href="/wiki/Environmental_impact_design" title="Environmental impact design">Environmental impact design</a></li> <li><a href="/wiki/Garden_design" title="Garden design">Garden design</a> <ul><li><a href="/wiki/Computer-aided_garden_design" title="Computer-aided garden design">Computer-aided</a></li></ul></li> <li><a href="/wiki/Healthy_community_design" title="Healthy community design">Healthy community design</a></li> <li><a href="/wiki/Hotel_design" title="Hotel design">Hotel design</a></li> <li><a href="/wiki/Interior_architecture" title="Interior architecture">Interior architecture</a></li> <li><a href="/wiki/Interior_design" title="Interior design">Interior design</a> <ul><li><a href="/wiki/Experiential_interior_design" title="Experiential interior design">EID</a></li></ul></li> <li><a href="/wiki/Keyline_design" title="Keyline design">Keyline design</a></li> <li><a href="/wiki/Landscape_architecture" title="Landscape architecture">Landscape architecture</a> <ul><li><a href="/wiki/Sustainable_landscape_architecture" title="Sustainable landscape architecture">Sustainable</a></li></ul></li> <li><a href="/wiki/Landscape_design" title="Landscape design">Landscape design</a></li> <li><a href="/wiki/Spatial_design" title="Spatial design">Spatial design</a></li> <li><a href="/wiki/Urban_design" title="Urban design">Urban design</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Industrial_design" title="Industrial design">Industrial<br />design</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Automotive_design" title="Automotive design">Automotive design</a></li> <li><a href="/wiki/Automotive_suspension_design_process" title="Automotive suspension design process">Automotive suspension design</a></li> <li><a href="/wiki/CMF_design" title="CMF design">CMF design</a></li> <li><a href="/wiki/Corrugated_box_design" title="Corrugated box design">Corrugated box design</a></li> <li><a href="/wiki/Electric_guitar_design" title="Electric guitar design">Electric guitar design</a></li> <li><a href="/wiki/Furniture" title="Furniture">Furniture design</a> <ul><li><a href="/wiki/Sustainable_furniture_design" title="Sustainable furniture design">Sustainable</a></li></ul></li> <li><a href="/wiki/Hardware_interface_design" title="Hardware interface design">Hardware interface design</a></li> <li><a href="/wiki/Motorcycle_design" title="Motorcycle design">Motorcycle design</a></li> <li><a href="/wiki/Packaging_and_labeling" class="mw-redirect" title="Packaging and labeling">Packaging and labeling</a></li> <li><a href="/wiki/Photographic_lens_design" title="Photographic lens design">Photographic lens design</a></li> <li><a href="/wiki/Product_design" title="Product design">Product design</a></li> <li><a href="/wiki/Production_designer" title="Production designer">Production design</a></li> <li><a href="/wiki/Sensory_design" title="Sensory design">Sensory design</a></li> <li><a href="/wiki/Service_design" title="Service design">Service design</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interaction_design" title="Interaction design">Interaction<br />design</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experience_design" class="mw-redirect" title="Experience design">Experience design</a> <ul><li><a href="/wiki/Employee_experience_design" title="Employee experience design">EED</a></li></ul></li> <li><a href="/wiki/Game_design" title="Game design">Game design</a> <ul><li><a href="/wiki/Level_(video_games)" title="Level (video games)">Level design</a></li> <li><a href="/wiki/Video_game_design" title="Video game design">Video game design</a></li></ul></li> <li><a href="/wiki/Hardware_interface_design" title="Hardware interface design">Hardware interface design</a></li> <li><a href="/wiki/Icon_design" title="Icon design">Icon design</a></li> <li><a href="/wiki/Immersive_design" title="Immersive design">Immersive design</a></li> <li><a href="/wiki/Information_design" title="Information design">Information design</a></li> <li><a href="/wiki/Sonic_interaction_design" title="Sonic interaction design">Sonic interaction design</a></li> <li><a href="/wiki/User_experience_design" title="User experience design">User experience design</a></li> <li><a href="/wiki/User_interface_design" title="User interface design">User interface design</a></li> <li><a href="/wiki/Web_design" title="Web design">Web design</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br /><a href="/wiki/Applied_arts" title="Applied arts">applied arts</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Public_art" title="Public art">Public art design</a></li> <li><a href="/wiki/Ceramic_art" title="Ceramic art">Ceramic</a> / <a href="/wiki/Glass_art" title="Glass art">glass design</a></li> <li><a href="/wiki/Fashion_design" title="Fashion design">Fashion design</a> <ul><li><a href="/wiki/Costume_design" title="Costume design">Costume design</a></li> <li><a href="/wiki/Jewellery_design" title="Jewellery design">Jewellery design</a></li></ul></li> <li><a href="/wiki/Floral_design" title="Floral design">Floral design</a></li> <li><a href="/wiki/Game_art_design" title="Game art design">Game art design</a></li> <li><a href="/wiki/Property_designer" class="mw-redirect" title="Property designer">Property design</a></li> <li><a href="/wiki/Scenic_design" title="Scenic design">Scenic design</a></li> <li><a href="/wiki/Sound_design" title="Sound design">Sound design</a></li> <li><a href="/wiki/Lighting_design" title="Lighting design">Stage/set lighting design</a></li> <li><a href="/wiki/Textile_design" title="Textile design">Textile design</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other<br />design<br />& <a href="/wiki/Engineering" title="Engineering">engineering</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithm_design" class="mw-redirect" title="Algorithm design">Algorithm design</a></li> <li><a href="/wiki/Behavioural_design" title="Behavioural design">Behavioural design</a></li> <li><a href="/wiki/Boiler_design" title="Boiler design">Boiler design</a></li> <li><a href="/wiki/Database_design" title="Database design">Database design</a></li> <li><a href="/wiki/Drug_design" title="Drug design">Drug design</a></li> <li><a href="/wiki/Electrical_system_design" title="Electrical system design">Electrical system design</a></li> <li><a href="/wiki/Design_of_experiments" title="Design of experiments">Experimental design</a></li> <li><a href="/wiki/Filter_design" title="Filter design">Filter design</a></li> <li><a href="/wiki/Geometric_design" title="Geometric design">Geometric design</a></li> <li><a href="/wiki/Work_design" title="Work design">Work design</a></li> <li><a href="/wiki/Integrated_circuit_design" title="Integrated circuit design">Integrated circuit design</a> <ul><li><a href="/wiki/Circuit_design" title="Circuit design">Circuit design</a></li> <li><a href="/wiki/Physical_design_(electronics)" title="Physical design (electronics)">Physical design</a></li> <li><a href="/wiki/Power_network_design_(IC)" title="Power network design (IC)">Power network design</a></li></ul></li> <li><a href="/wiki/Mechanism_design" title="Mechanism design">Mechanism design</a></li> <li><a href="/wiki/Nuclear_weapon_design" title="Nuclear weapon design">Nuclear weapon design</a></li> <li><a href="/wiki/Nucleic_acid_design" title="Nucleic acid design">Nucleic acid design</a></li> <li><a href="/wiki/Organizational_architecture" title="Organizational architecture">Organization design</a></li> <li><a href="/wiki/Process_design" title="Process design">Process design</a></li> <li><a href="/wiki/Processor_design" title="Processor design">Processor design</a></li> <li><a href="/wiki/Protein_design" title="Protein design">Protein design</a></li> <li><a href="/wiki/Research_design" title="Research design">Research design</a></li> <li><a href="/wiki/Social_design" title="Social design">Social design</a></li> <li><a href="/wiki/Software_design" title="Software design">Software design</a></li> <li><a href="/wiki/Spacecraft_design" title="Spacecraft design">Spacecraft design</a></li> <li><a href="/wiki/Strategic_design" title="Strategic design">Strategic design</a></li> <li><a href="/wiki/Systems_design" title="Systems design">Systems design</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Approaches" style="font-size:114%;margin:0 4em">Approaches</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Activity-centered_design" title="Activity-centered design">Activity-centered</a></li> <li><a href="/wiki/Adaptive_web_design" title="Adaptive web design">Adaptive web</a></li> <li><a href="/wiki/Affective_design" title="Affective design">Affective</a></li> <li><a href="/wiki/Brainstorming" title="Brainstorming">Brainstorming</a></li> <li><a href="/wiki/Design_by_committee" title="Design by committee">By committee</a></li> <li><a href="/wiki/Design_by_contract" title="Design by contract">By contract</a></li> <li><a href="/wiki/C-K_theory" title="C-K theory">C-K theory</a></li> <li><a href="/wiki/Design_closure" title="Design closure">Closure</a></li> <li><a href="/wiki/Participatory_design" title="Participatory design">Co-design</a></li> <li><a href="/w/index.php?title=Concept-oriented_design&action=edit&redlink=1" class="new" title="Concept-oriented design (page does not exist)">Concept-oriented</a></li> <li><a href="/wiki/Configuration_design" title="Configuration design">Configuration</a></li> <li><a href="/wiki/Contextual_design" title="Contextual design">Contextual</a></li> <li><a href="/wiki/Continuous_design" title="Continuous design">Continuous</a></li> <li><a href="/wiki/Cradle-to-cradle_design" title="Cradle-to-cradle design">Cradle-to-cradle</a></li> <li><a href="/wiki/Creative_problem-solving" title="Creative problem-solving">Creative problem-solving</a></li> <li><a href="/wiki/Creativity_techniques" title="Creativity techniques">Creativity techniques</a></li> <li><a href="/wiki/Critical_design" title="Critical design">Critical</a> <ul><li><a href="/wiki/Design_fiction" title="Design fiction">Design fiction</a></li></ul></li> <li><a href="/wiki/Defensive_design" title="Defensive design">Defensive</a></li> <li><a href="/wiki/Design%E2%80%93bid%E2%80%93build" title="Design–bid–build">Design–bid–build</a></li> <li><a href="/wiki/Design%E2%80%93build" title="Design–build">Design–build</a> <ul><li><a href="/wiki/Architect-led_design%E2%80%93build" class="mw-redirect" title="Architect-led design–build">architect-led</a></li></ul></li> <li><a href="/wiki/Diffuse_design" title="Diffuse design">Diffuse</a></li> <li><a href="/wiki/Domain-driven_design" title="Domain-driven design">Domain-driven</a></li> <li><a href="/wiki/Ecological_design" title="Ecological design">Ecological design</a></li> <li><a href="/wiki/Energy_neutral_design" title="Energy neutral design">Energy neutral</a></li> <li><a href="/wiki/Engineering_design_process" title="Engineering design process">Engineering design process</a> <ul><li><a href="/wiki/Probabilistic_design" title="Probabilistic design">Probabilistic design</a></li></ul></li> <li><a href="/wiki/Error-tolerant_design" title="Error-tolerant design">Error-tolerant</a></li> <li><a href="/wiki/Fault-tolerant_design" class="mw-redirect" title="Fault-tolerant design">Fault-tolerant</a></li> <li><a href="/wiki/Framework-oriented_design" title="Framework-oriented design">Framework-oriented</a></li> <li><a href="/wiki/Design_for_assembly" title="Design for assembly">For assembly</a></li> <li><a href="/wiki/Behavioural_design" title="Behavioural design">For behaviour change</a></li> <li><a href="/wiki/Design_for_manufacturability" title="Design for manufacturability">For manufacturability</a></li> <li><a href="/wiki/Design_for_Six_Sigma" title="Design for Six Sigma">For Six Sigma</a></li> <li><a href="/wiki/Design_for_testing" title="Design for testing">For testing</a></li> <li><a href="/wiki/Design_for_X" title="Design for X">For X</a></li> <li><a href="/wiki/Functional_design" title="Functional design">Functional</a></li> <li><a href="/wiki/Generative_design" title="Generative design">Generative</a></li> <li><a href="/wiki/Geodesign" title="Geodesign">Geodesign</a></li> <li><a href="/wiki/Human-centered_design" title="Human-centered design">HCD</a></li> <li><a href="/wiki/High-level_design" title="High-level design">High-level</a></li> <li><a href="/wiki/Inclusive_design" title="Inclusive design">Inclusive</a></li> <li><a href="/wiki/Integrated_design" title="Integrated design">Integrated</a></li> <li><a href="/wiki/Integrated_topside_design" title="Integrated topside design">Integrated topside</a></li> <li><a href="/wiki/Intelligence-based_design" title="Intelligence-based design">Intelligence-based</a></li> <li><a href="/wiki/Iterative_design" title="Iterative design">Iterative</a></li> <li><a href="/wiki/KISS_principle" title="KISS principle">KISS principle</a></li> <li><a href="/wiki/Low-level_design" title="Low-level design">Low-level</a></li> <li><a href="/wiki/Metadesign" title="Metadesign">Metadesign</a></li> <li><a href="/wiki/Mind_map" title="Mind map">Mind mapping</a></li> <li><a href="/wiki/Modular_design" title="Modular design">Modular</a></li> <li><a href="/wiki/New_Wave_(design)" title="New Wave (design)">New Wave</a></li> <li><a href="/wiki/Object-oriented_design" class="mw-redirect" title="Object-oriented design">Object-oriented</a></li> <li><a href="/wiki/Open-design_movement" title="Open-design movement">Open</a></li> <li><a href="/wiki/Parametric_design" title="Parametric design">Parametric</a></li> <li><a href="/wiki/Participatory_design" title="Participatory design">Participatory</a></li> <li><a href="/wiki/Platform-based_design" title="Platform-based design">Platform-based</a></li> <li><a href="/wiki/Policy-based_design" class="mw-redirect" title="Policy-based design">Policy-based</a></li> <li><a href="/wiki/Process-centered_design" title="Process-centered design">Process-centered</a></li> <li><a href="/wiki/Public_interest_design" title="Public interest design">Public interest</a></li> <li><a href="/wiki/Rational_design" title="Rational design">Rational</a></li> <li><a href="/wiki/Regenerative_design" title="Regenerative design">Regenerative</a></li> <li><a class="mw-selflink selflink">Reliability engineering</a></li> <li><a href="/wiki/Research-based_design" title="Research-based design">Research-based</a></li> <li><a href="/wiki/Responsibility-driven_design" title="Responsibility-driven design">Responsibility-driven</a></li> <li><a href="/wiki/Responsive_web_design" title="Responsive web design">RWD</a></li> <li><a href="/wiki/Safe-life_design" title="Safe-life design">Safe-life</a></li> <li><a href="/wiki/Sustainable_design" title="Sustainable design">Sustainable</a></li> <li><a href="/wiki/Systemic_design" title="Systemic design">Systemic</a> <ul><li><a href="/wiki/Systems-oriented_design" title="Systems-oriented design">SOD</a></li></ul></li> <li><a href="/wiki/Tableless_web_design" title="Tableless web design">Tableless web</a></li> <li><a href="/wiki/Theory_of_constraints" title="Theory of constraints">Theory of constraints</a></li> <li><a href="/wiki/Top-down_and_bottom-up_design" class="mw-redirect" title="Top-down and bottom-up design">Top-down and bottom-up</a></li> <li><a href="/wiki/Transformation_design" title="Transformation design">Transformation</a></li> <li><a href="/wiki/Transgenerational_design" title="Transgenerational design">Transgenerational</a></li> <li><a href="/wiki/TRIZ" title="TRIZ">TRIZ</a></li> <li><a href="/wiki/Universal_design" title="Universal design">Universal</a> <ul><li><a href="/wiki/Design_for_All_(in_ICT)" title="Design for All (in ICT)">Design for All</a></li></ul></li> <li><a href="/wiki/Usage-centered_design" title="Usage-centered design">Usage-centered</a></li> <li><a href="/wiki/Use-centered_design" title="Use-centered design">Use-centered</a></li> <li><a href="/wiki/User-centered_design" title="User-centered design">User-centered</a> <ul><li><a href="/wiki/Empathic_design" title="Empathic design">Empathic</a></li></ul></li> <li><a href="/wiki/User_innovation" title="User innovation">User innovation</a></li> <li><a href="/wiki/Value-driven_design" title="Value-driven design">Value-driven</a></li> <li><a href="/wiki/Value_sensitive_design" title="Value sensitive design">Value sensitive</a> <ul><li><a href="/wiki/Privacy_by_design" title="Privacy by design">Privacy by</a></li></ul></li></ul> <ul><li>Design <a href="/wiki/Design_choice" title="Design choice">choice</a></li> <li><a href="/wiki/Design_computing" title="Design computing">computing</a></li> <li><a href="/wiki/Design_controls" title="Design controls">controls</a></li> <li><a href="/wiki/Design_culture" title="Design culture">culture</a></li> <li><a href="/wiki/Design_flow_(EDA)" title="Design flow (EDA)">flow</a></li> <li><a href="/wiki/Design_leadership" title="Design leadership">leadership</a></li> <li><a href="/wiki/Design_management" title="Design management">management</a></li> <li><a href="/wiki/Design_marker" title="Design marker">marker</a></li> <li><a href="/wiki/Design_methods" title="Design methods">methods</a></li> <li><a href="/wiki/Design_pattern" title="Design pattern">pattern</a></li> <li><a href="/wiki/Design_research" title="Design research">research</a></li> <li><a href="/wiki/Design_science" title="Design science">science</a></li> <li><a href="/wiki/Design_sprint" title="Design sprint">sprint</a></li> <li><a href="/wiki/Design_strategy" class="mw-redirect" title="Design strategy">strategy</a></li> <li><a href="/wiki/Design_theory" title="Design theory">theory</a></li> <li><a href="/wiki/Design_thinking" title="Design thinking">thinking</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="ToolsIntellectual_propertyOrganizationsAwards" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li>Tools</li><li>Intellectual property</li><li>Organizations</li><li>Awards</li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Design_tool" title="Design tool">Tools</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithms-Aided_Design" title="Algorithms-Aided Design">AAD</a></li> <li><a href="/wiki/Architectural_model" title="Architectural model">Architectural model</a></li> <li><a href="/wiki/Blueprint" title="Blueprint">Blueprint</a></li> <li><a href="/wiki/Comprehensive_layout" title="Comprehensive layout">Comprehensive layout</a></li> <li><a href="/wiki/Computer-aided_design" title="Computer-aided design">CAD</a> <ul><li><a href="/wiki/Computer-aided_industrial_design" title="Computer-aided industrial design">CAID</a></li> <li><a href="/wiki/Virtual_home_design_software" title="Virtual home design software">Virtual home design software</a></li></ul></li> <li><a href="/wiki/Computer-automated_design" title="Computer-automated design">CAutoD</a></li> <li><a href="/wiki/Design_quality_indicator" title="Design quality indicator">Design quality indicator</a></li> <li><a href="/wiki/Electronic_design_automation" title="Electronic design automation">Electronic design automation</a></li> <li><a href="/wiki/Flowchart" title="Flowchart">Flowchart</a></li> <li><a href="/wiki/Mockup" title="Mockup">Mockup</a></li> <li><a href="/wiki/Design_specification" title="Design specification">Design specification</a></li> <li><a href="/wiki/Prototype" title="Prototype">Prototype</a></li> <li><a href="/wiki/Sketch_(drawing)" title="Sketch (drawing)">Sketch</a></li> <li><a href="/wiki/Storyboard" title="Storyboard">Storyboard</a></li> <li><a href="/wiki/Technical_drawing" title="Technical drawing">Technical drawing</a></li> <li><a href="/wiki/HTML_editor" title="HTML editor">HTML editor</a></li> <li><a href="/wiki/Website_wireframe" title="Website wireframe">Website wireframe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Intellectual<br />property</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Community_design" title="Community design">Community design</a></li> <li><a href="/wiki/Design_around" title="Design around">Design around</a></li> <li><a href="/wiki/Design_infringement" title="Design infringement">Design infringement</a></li> <li><a href="/wiki/Design_patent" title="Design patent">Design patent</a></li> <li><a href="/wiki/Fashion_design_copyright" title="Fashion design copyright">Fashion design copyright</a></li> <li><i><a href="/wiki/Geschmacksmuster" title="Geschmacksmuster">Geschmacksmuster</a></i></li> <li><a href="/wiki/Industrial_design_right" title="Industrial design right">Industrial design rights</a> <ul><li><a href="/wiki/Industrial_design_rights_in_the_European_Union" title="Industrial design rights in the European Union">European Union</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/American_Institute_of_Graphic_Arts" title="American Institute of Graphic Arts">American Institute of Graphic Arts</a></li> <li><a href="/wiki/Chartered_Society_of_Designers" title="Chartered Society of Designers">Chartered Society of Designers</a></li> <li><a href="/wiki/Design_and_Industries_Association" title="Design and Industries Association">Design and Industries Association</a></li> <li><a href="/wiki/Design_Council" title="Design Council">Design Council</a></li> <li><a href="/wiki/International_Forum_Design" title="International Forum Design">International Forum Design</a></li> <li><a href="/wiki/Design_Research_Society" title="Design Research Society">Design Research Society</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Awards</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/European_Design_Award" class="mw-redirect" title="European Design Award">European Design Award</a></li> <li><a href="/wiki/German_Design_Award" title="German Design Award">German Design Award</a></li> <li><a href="/wiki/Good_Design_Award_(Museum_of_Modern_Art)" title="Good Design Award (Museum of Modern Art)">Good Design Award (Museum of Modern Art)</a></li> <li><a href="/wiki/Good_Design_Award_(Chicago_Athenaeum)" class="mw-redirect" title="Good Design Award (Chicago Athenaeum)">Good Design Award (Chicago Athenaeum)</a></li> <li><a href="/wiki/Graphex" class="mw-redirect" title="Graphex">Graphex</a></li> <li><a href="/wiki/IF_Product_Design_Award" title="IF Product Design Award">IF Product Design Award</a></li> <li><a href="/wiki/James_Dyson_Award" title="James Dyson Award">James Dyson Award</a></li> <li><a href="/wiki/Prince_Philip_Designers_Prize" title="Prince Philip Designers Prize">Prince Philip Designers Prize</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Related_topics" style="font-size:114%;margin:0 4em">Related topics</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Agile_software_development" title="Agile software development">Agile</a></li> <li><a href="/wiki/Concept_art" title="Concept art">Concept art</a></li> <li><a href="/wiki/Conceptual_design" title="Conceptual design">Conceptual design</a></li> <li><a href="/wiki/Creative_industries" title="Creative industries">Creative industries</a></li> <li><a href="/wiki/Cultural_icon" title="Cultural icon">Cultural icon</a></li> <li><a href="/wiki/.design" title=".design">.design</a></li> <li><a href="/wiki/Enterprise_architecture" title="Enterprise architecture">Enterprise architecture</a></li> <li><a href="/wiki/Form_factor_(design)" title="Form factor (design)">Form factor</a></li> <li><a href="/wiki/Futures_studies" title="Futures studies">Futures studies</a></li> <li><a href="/wiki/Indie_design" title="Indie design">Indie design</a></li> <li><a href="/wiki/Innovation_management" title="Innovation management">Innovation management</a></li> <li><a href="/wiki/Intelligent_design" title="Intelligent design">Intelligent design</a></li> <li><a href="/wiki/Lean_startup" title="Lean startup">Lean startup</a></li> <li><a href="/wiki/New_product_development" title="New product development">New product development</a></li> <li><a href="/wiki/OODA_loop" title="OODA loop">OODA loop</a></li> <li><a href="/wiki/Philosophy_of_design" title="Philosophy of design">Philosophy of design</a></li> <li><a href="/wiki/Process_simulation" title="Process simulation">Process simulation</a></li> <li><a href="/wiki/Slow_design" class="mw-redirect" title="Slow design">Slow design</a></li> <li><a href="/wiki/STEAM_fields" class="mw-redirect" title="STEAM fields">STEAM fields</a></li> <li><a href="/wiki/Argument_from_poor_design" title="Argument from poor design">Unintelligent design</a></li> <li><a href="/wiki/Visualization_(graphics)" title="Visualization (graphics)">Visualization</a></li> <li><a href="/wiki/Wicked_problem" title="Wicked problem">Wicked problem</a></li></ul> <ul><li>Design <a href="/wiki/Design_brief" title="Design brief">brief</a></li> <li><a href="/wiki/Design_change" title="Design change">change</a></li> <li><a href="/wiki/Design_classic" title="Design classic">classic</a></li> <li><a href="/wiki/Design_competition" title="Design competition">competition</a> <ul><li><a href="/wiki/Architectural_design_competition" title="Architectural design competition">architectural</a></li> <li><a href="/wiki/Student_design_competition" title="Student design competition">student</a></li></ul></li> <li><a href="/wiki/Design_director" title="Design director">director</a></li> <li><a href="/wiki/Design_education" title="Design education">education</a></li> <li><a href="/wiki/Design_elements" title="Design elements">elements</a></li> <li><a href="/wiki/Design_engineer" title="Design engineer">engineer</a></li> <li><a href="/wiki/Design_firm" class="mw-redirect" title="Design firm">firm</a></li> <li><a href="/wiki/Design_history" title="Design history">history</a></li> <li><a href="/wiki/Design_knowledge" title="Design knowledge">knowledge</a></li> <li><a href="/wiki/Design_language" title="Design language">language</a></li> <li><a href="/wiki/Design_life" title="Design life">life</a></li> <li><a href="/wiki/Design_load" title="Design load">load</a></li> <li><a href="/wiki/Design_museum" title="Design museum">museum</a></li> <li><a href="/wiki/Design_paradigm" title="Design paradigm">paradigm</a></li> <li><a href="/wiki/Design_principles" title="Design principles">principles</a></li> <li><a href="/wiki/Design_rationale" title="Design rationale">rationale</a></li> <li><a href="/wiki/Design_review" title="Design review">review</a></li> <li><a href="/wiki/Design_specification" title="Design specification">specification</a></li> <li><a href="/wiki/Design_studies" title="Design studies">studies</a></li> <li><a href="/wiki/Design_studio" class="mw-redirect" title="Design studio">studio</a></li> <li><a href="/wiki/Design_technology" title="Design technology">technology</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="https://commons.wikimedia.org/wiki/category:Design" class="extiw" title="commons:category:Design"> <span class="tmp-color" style="color:#002bb8">Commons</span> </a></li> <li><a href="https://en.wikibooks.org/wiki/Design" class="extiw" title="wikibooks:Design"> <span class="tmp-color" style="color:#002bb8">Wikibooks</span> </a></li> <li><a href="https://en.wikinews.org/wiki/Special:Search/Design" class="extiw" title="wikinews:Special:Search/Design"> <span class="tmp-color" style="color:#002bb8">Wikinews</span> </a></li> <li><a href="https://en.wikiquote.org/wiki/Design" class="extiw" title="wikiquote:Design"> <span class="tmp-color" style="color:#002bb8">Wikiquote</span> </a></li> <li><a href="https://en.wikisource.org/wiki/Category:Design" class="extiw" title="wikisource:Category:Design"> <span class="tmp-color" style="color:#002bb8">Wikisource</span> </a></li> <li><a href="https://en.wiktionary.org/wiki/Design" class="extiw" title="wiktionary:Design"> <span class="tmp-color" style="color:#002bb8">Wiktionary</span> </a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Statistics" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Statistics" title="Template:Statistics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Statistics" title="Template talk:Statistics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Statistics" title="Special:EditPage/Template:Statistics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Statistics" style="font-size:114%;margin:0 4em"><a href="/wiki/Statistics" title="Statistics">Statistics</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Outline_of_statistics" title="Outline of statistics">Outline</a></li> <li><a href="/wiki/List_of_statistics_articles" title="List of statistics articles">Index</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Descriptive_statistics" style="font-size:114%;margin:0 4em"><a href="/wiki/Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">Continuous data</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Central_tendency" title="Central tendency">Center</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mean" title="Mean">Mean</a> <ul><li><a href="/wiki/Arithmetic_mean" title="Arithmetic mean">Arithmetic</a></li> <li><a href="/wiki/Arithmetic%E2%80%93geometric_mean" title="Arithmetic–geometric mean">Arithmetic-Geometric</a></li> <li><a href="/wiki/Contraharmonic_mean" title="Contraharmonic mean">Contraharmonic</a></li> <li><a href="/wiki/Cubic_mean" title="Cubic mean">Cubic</a></li> <li><a href="/wiki/Generalized_mean" title="Generalized mean">Generalized/power</a></li> <li><a href="/wiki/Geometric_mean" title="Geometric mean">Geometric</a></li> <li><a href="/wiki/Harmonic_mean" title="Harmonic mean">Harmonic</a></li> <li><a href="/wiki/Heronian_mean" title="Heronian mean">Heronian</a></li> <li><a href="/wiki/Heinz_mean" title="Heinz mean">Heinz</a></li> <li><a href="/wiki/Lehmer_mean" title="Lehmer mean">Lehmer</a></li></ul></li> <li><a href="/wiki/Median" title="Median">Median</a></li> <li><a href="/wiki/Mode_(statistics)" title="Mode (statistics)">Mode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_dispersion" title="Statistical dispersion">Dispersion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Average_absolute_deviation" title="Average absolute deviation">Average absolute deviation</a></li> <li><a href="/wiki/Coefficient_of_variation" title="Coefficient of variation">Coefficient of variation</a></li> <li><a href="/wiki/Interquartile_range" title="Interquartile range">Interquartile range</a></li> <li><a href="/wiki/Percentile" title="Percentile">Percentile</a></li> <li><a href="/wiki/Range_(statistics)" title="Range (statistics)">Range</a></li> <li><a href="/wiki/Standard_deviation" title="Standard deviation">Standard deviation</a></li> <li><a href="/wiki/Variance#Sample_variance" title="Variance">Variance</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Shape_of_the_distribution" class="mw-redirect" title="Shape of the distribution">Shape</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Central_limit_theorem" title="Central limit theorem">Central limit theorem</a></li> <li><a href="/wiki/Moment_(mathematics)" title="Moment (mathematics)">Moments</a> <ul><li><a href="/wiki/Kurtosis" title="Kurtosis">Kurtosis</a></li> <li><a href="/wiki/L-moment" title="L-moment">L-moments</a></li> <li><a href="/wiki/Skewness" title="Skewness">Skewness</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Count_data" title="Count data">Count data</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Index_of_dispersion" title="Index of dispersion">Index of dispersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Summary tables</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Frequency_distribution" class="mw-redirect" title="Frequency distribution">Frequency distribution</a></li> <li><a href="/wiki/Grouped_data" title="Grouped data">Grouped data</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Dependence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Pearson_correlation_coefficient" title="Pearson correlation coefficient">Pearson product-moment correlation</a></li> <li><a href="/wiki/Rank_correlation" title="Rank correlation">Rank correlation</a> <ul><li><a href="/wiki/Kendall_rank_correlation_coefficient" title="Kendall rank correlation coefficient">Kendall's τ</a></li> <li><a href="/wiki/Spearman%27s_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's ρ</a></li></ul></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_graphics" title="Statistical graphics">Graphics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bar_chart" title="Bar chart">Bar chart</a></li> <li><a href="/wiki/Biplot" title="Biplot">Biplot</a></li> <li><a href="/wiki/Box_plot" title="Box plot">Box plot</a></li> <li><a href="/wiki/Control_chart" title="Control chart">Control chart</a></li> <li><a href="/wiki/Correlogram" title="Correlogram">Correlogram</a></li> <li><a href="/wiki/Fan_chart_(statistics)" title="Fan chart (statistics)">Fan chart</a></li> <li><a href="/wiki/Forest_plot" title="Forest plot">Forest plot</a></li> <li><a href="/wiki/Histogram" title="Histogram">Histogram</a></li> <li><a href="/wiki/Pie_chart" title="Pie chart">Pie chart</a></li> <li><a href="/wiki/Q%E2%80%93Q_plot" title="Q–Q plot">Q–Q plot</a></li> <li><a href="/wiki/Radar_chart" title="Radar chart">Radar chart</a></li> <li><a href="/wiki/Run_chart" title="Run chart">Run chart</a></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li> <li><a href="/wiki/Stem-and-leaf_display" title="Stem-and-leaf display">Stem-and-leaf display</a></li> <li><a href="/wiki/Violin_plot" title="Violin plot">Violin plot</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_collection" style="font-size:114%;margin:0 4em"><a href="/wiki/Data_collection" title="Data collection">Data collection</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Design_of_experiments" title="Design of experiments">Study design</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Effect_size" title="Effect size">Effect size</a></li> <li><a href="/wiki/Missing_data" title="Missing data">Missing data</a></li> <li><a href="/wiki/Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a></li> <li><a href="/wiki/Statistical_population" title="Statistical population">Population</a></li> <li><a href="/wiki/Replication_(statistics)" title="Replication (statistics)">Replication</a></li> <li><a href="/wiki/Sample_size_determination" title="Sample size determination">Sample size determination</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">Statistical power</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survey_methodology" title="Survey methodology">Survey methodology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">Sampling</a> <ul><li><a href="/wiki/Cluster_sampling" title="Cluster sampling">Cluster</a></li> <li><a href="/wiki/Stratified_sampling" title="Stratified sampling">Stratified</a></li></ul></li> <li><a href="/wiki/Opinion_poll" title="Opinion poll">Opinion poll</a></li> <li><a href="/wiki/Questionnaire" title="Questionnaire">Questionnaire</a></li> <li><a href="/wiki/Standard_error" title="Standard error">Standard error</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Experiment" title="Experiment">Controlled experiments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></li> <li><a href="/wiki/Factorial_experiment" title="Factorial experiment">Factorial experiment</a></li> <li><a href="/wiki/Interaction_(statistics)" title="Interaction (statistics)">Interaction</a></li> <li><a href="/wiki/Random_assignment" title="Random assignment">Random assignment</a></li> <li><a href="/wiki/Randomized_controlled_trial" title="Randomized controlled trial">Randomized controlled trial</a></li> <li><a href="/wiki/Randomized_experiment" title="Randomized experiment">Randomized experiment</a></li> <li><a href="/wiki/Scientific_control" title="Scientific control">Scientific control</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Adaptive designs</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a></li> <li><a href="/wiki/Stochastic_approximation" title="Stochastic approximation">Stochastic approximation</a></li> <li><a href="/wiki/Up-and-Down_Designs" class="mw-redirect" title="Up-and-Down Designs">Up-and-down designs</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Observational_study" title="Observational study">Observational studies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohort_study" title="Cohort study">Cohort study</a></li> <li><a href="/wiki/Cross-sectional_study" title="Cross-sectional study">Cross-sectional study</a></li> <li><a href="/wiki/Natural_experiment" title="Natural experiment">Natural experiment</a></li> <li><a href="/wiki/Quasi-experiment" title="Quasi-experiment">Quasi-experiment</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistical_inference" style="font-size:114%;margin:0 4em"><a href="/wiki/Statistical_inference" title="Statistical inference">Statistical inference</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_theory" title="Statistical theory">Statistical theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Population_(statistics)" class="mw-redirect" title="Population (statistics)">Population</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Probability_distribution" title="Probability distribution">Probability distribution</a></li> <li><a href="/wiki/Sampling_distribution" title="Sampling distribution">Sampling distribution</a> <ul><li><a href="/wiki/Order_statistic" title="Order statistic">Order statistic</a></li></ul></li> <li><a href="/wiki/Empirical_distribution_function" title="Empirical distribution function">Empirical distribution</a> <ul><li><a href="/wiki/Density_estimation" title="Density estimation">Density estimation</a></li></ul></li> <li><a href="/wiki/Statistical_model" title="Statistical model">Statistical model</a> <ul><li><a href="/wiki/Model_specification" class="mw-redirect" title="Model specification">Model specification</a></li> <li><a href="/wiki/Lp_space" title="Lp space">L<sup><i>p</i></sup> space</a></li></ul></li> <li><a href="/wiki/Statistical_parameter" title="Statistical parameter">Parameter</a> <ul><li><a href="/wiki/Location_parameter" title="Location parameter">location</a></li> <li><a href="/wiki/Scale_parameter" title="Scale parameter">scale</a></li> <li><a href="/wiki/Shape_parameter" title="Shape parameter">shape</a></li></ul></li> <li><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric family</a> <ul><li><a href="/wiki/Likelihood_function" title="Likelihood function">Likelihood</a> <a href="/wiki/Monotone_likelihood_ratio" title="Monotone likelihood ratio"><span style="font-size:85%;">(monotone)</span></a></li> <li><a href="/wiki/Location%E2%80%93scale_family" title="Location–scale family">Location–scale family</a></li> <li><a href="/wiki/Exponential_family" title="Exponential family">Exponential family</a></li></ul></li> <li><a href="/wiki/Completeness_(statistics)" title="Completeness (statistics)">Completeness</a></li> <li><a href="/wiki/Sufficient_statistic" title="Sufficient statistic">Sufficiency</a></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Statistical functional</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/U-statistic" title="U-statistic">U</a></li> <li><a href="/wiki/V-statistic" title="V-statistic">V</a></li></ul></li> <li><a href="/wiki/Optimal_decision" title="Optimal decision">Optimal decision</a> <ul><li><a href="/wiki/Loss_function" title="Loss function">loss function</a></li></ul></li> <li><a href="/wiki/Efficiency_(statistics)" title="Efficiency (statistics)">Efficiency</a></li> <li><a href="/wiki/Statistical_distance" title="Statistical distance">Statistical distance</a> <ul><li><a href="/wiki/Divergence_(statistics)" title="Divergence (statistics)">divergence</a></li></ul></li> <li><a href="/wiki/Asymptotic_theory_(statistics)" title="Asymptotic theory (statistics)">Asymptotics</a></li> <li><a href="/wiki/Robust_statistics" title="Robust statistics">Robustness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Frequentist_inference" title="Frequentist inference">Frequentist inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Point_estimation" title="Point estimation">Point estimation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Estimating_equations" title="Estimating equations">Estimating equations</a> <ul><li><a href="/wiki/Maximum_likelihood" class="mw-redirect" title="Maximum likelihood">Maximum likelihood</a></li> <li><a href="/wiki/Method_of_moments_(statistics)" title="Method of moments (statistics)">Method of moments</a></li> <li><a href="/wiki/M-estimator" title="M-estimator">M-estimator</a></li> <li><a href="/wiki/Minimum_distance_estimation" class="mw-redirect" title="Minimum distance estimation">Minimum distance</a></li></ul></li> <li><a href="/wiki/Bias_of_an_estimator" title="Bias of an estimator">Unbiased estimators</a> <ul><li><a href="/wiki/Minimum-variance_unbiased_estimator" title="Minimum-variance unbiased estimator">Mean-unbiased minimum-variance</a> <ul><li><a href="/wiki/Rao%E2%80%93Blackwell_theorem" title="Rao–Blackwell theorem">Rao–Blackwellization</a></li> <li><a href="/wiki/Lehmann%E2%80%93Scheff%C3%A9_theorem" title="Lehmann–Scheffé theorem">Lehmann–Scheffé theorem</a></li></ul></li> <li><a href="/wiki/Median-unbiased_estimator" class="mw-redirect" title="Median-unbiased estimator">Median unbiased</a></li></ul></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Plug-in</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Interval_estimation" title="Interval estimation">Interval estimation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Confidence_interval" title="Confidence interval">Confidence interval</a></li> <li><a href="/wiki/Pivotal_quantity" title="Pivotal quantity">Pivot</a></li> <li><a href="/wiki/Likelihood_interval" class="mw-redirect" title="Likelihood interval">Likelihood interval</a></li> <li><a href="/wiki/Prediction_interval" title="Prediction interval">Prediction interval</a></li> <li><a href="/wiki/Tolerance_interval" title="Tolerance interval">Tolerance interval</a></li> <li><a href="/wiki/Resampling_(statistics)" title="Resampling (statistics)">Resampling</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/Jackknife_resampling" title="Jackknife resampling">Jackknife</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Testing hypotheses</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/One-_and_two-tailed_tests" title="One- and two-tailed tests">1- & 2-tails</a></li> <li><a href="/wiki/Power_(statistics)" title="Power (statistics)">Power</a> <ul><li><a href="/wiki/Uniformly_most_powerful_test" title="Uniformly most powerful test">Uniformly most powerful test</a></li></ul></li> <li><a href="/wiki/Permutation_test" title="Permutation test">Permutation test</a> <ul><li><a href="/wiki/Randomization_test" class="mw-redirect" title="Randomization test">Randomization test</a></li></ul></li> <li><a href="/wiki/Multiple_comparisons" class="mw-redirect" title="Multiple comparisons">Multiple comparisons</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio</a></li> <li><a href="/wiki/Score_test" title="Score test">Score/Lagrange multiplier</a></li> <li><a href="/wiki/Wald_test" title="Wald test">Wald</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/List_of_statistical_tests" title="List of statistical tests">Specific tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Z-test" title="Z-test"><i>Z</i>-test <span style="font-size:85%;">(normal)</span></a></li> <li><a href="/wiki/Student%27s_t-test" title="Student's t-test">Student's <i>t</i>-test</a></li> <li><a href="/wiki/F-test" title="F-test"><i>F</i>-test</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Goodness_of_fit" title="Goodness of fit">Goodness of fit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chi-squared_test" title="Chi-squared test">Chi-squared</a></li> <li><a href="/wiki/G-test" title="G-test"><i>G</i>-test</a></li> <li><a href="/wiki/Kolmogorov%E2%80%93Smirnov_test" title="Kolmogorov–Smirnov test">Kolmogorov–Smirnov</a></li> <li><a href="/wiki/Anderson%E2%80%93Darling_test" title="Anderson–Darling test">Anderson–Darling</a></li> <li><a href="/wiki/Lilliefors_test" title="Lilliefors test">Lilliefors</a></li> <li><a href="/wiki/Jarque%E2%80%93Bera_test" title="Jarque–Bera test">Jarque–Bera</a></li> <li><a href="/wiki/Shapiro%E2%80%93Wilk_test" title="Shapiro–Wilk test">Normality <span style="font-size:85%;">(Shapiro–Wilk)</span></a></li> <li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio test</a></li> <li><a href="/wiki/Model_selection" title="Model selection">Model selection</a> <ul><li><a href="/wiki/Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross validation</a></li> <li><a href="/wiki/Akaike_information_criterion" title="Akaike information criterion">AIC</a></li> <li><a href="/wiki/Bayesian_information_criterion" title="Bayesian information criterion">BIC</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Rank_statistics" class="mw-redirect" title="Rank statistics">Rank statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sign_test" title="Sign test">Sign</a> <ul><li><a href="/wiki/Sample_median" class="mw-redirect" title="Sample median">Sample median</a></li></ul></li> <li><a href="/wiki/Wilcoxon_signed-rank_test" title="Wilcoxon signed-rank test">Signed rank <span style="font-size:85%;">(Wilcoxon)</span></a> <ul><li><a href="/wiki/Hodges%E2%80%93Lehmann_estimator" title="Hodges–Lehmann estimator">Hodges–Lehmann estimator</a></li></ul></li> <li><a href="/wiki/Mann%E2%80%93Whitney_U_test" title="Mann–Whitney U test">Rank sum <span style="font-size:85%;">(Mann–Whitney)</span></a></li> <li><a href="/wiki/Nonparametric_statistics" title="Nonparametric statistics">Nonparametric</a> <a href="/wiki/Analysis_of_variance" title="Analysis of variance">anova</a> <ul><li><a href="/wiki/Kruskal%E2%80%93Wallis_test" title="Kruskal–Wallis test">1-way <span style="font-size:85%;">(Kruskal–Wallis)</span></a></li> <li><a href="/wiki/Friedman_test" title="Friedman test">2-way <span style="font-size:85%;">(Friedman)</span></a></li> <li><a href="/wiki/Jonckheere%27s_trend_test" title="Jonckheere's trend test">Ordered alternative <span style="font-size:85%;">(Jonckheere–Terpstra)</span></a></li></ul></li> <li><a href="/wiki/Van_der_Waerden_test" title="Van der Waerden test">Van der Waerden test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bayesian_probability" title="Bayesian probability">Bayesian probability</a> <ul><li><a href="/wiki/Prior_probability" title="Prior probability">prior</a></li> <li><a href="/wiki/Posterior_probability" title="Posterior probability">posterior</a></li></ul></li> <li><a href="/wiki/Credible_interval" title="Credible interval">Credible interval</a></li> <li><a href="/wiki/Bayes_factor" title="Bayes factor">Bayes factor</a></li> <li><a href="/wiki/Bayes_estimator" title="Bayes estimator">Bayesian estimator</a> <ul><li><a href="/wiki/Maximum_a_posteriori_estimation" title="Maximum a posteriori estimation">Maximum posterior estimator</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="CorrelationRegression_analysis" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></li><li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment</a></li> <li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Confounding" title="Confounding">Confounding variable</a></li> <li><a href="/wiki/Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Errors_and_residuals" title="Errors and residuals">Errors and residuals</a></li> <li><a href="/wiki/Regression_validation" title="Regression validation">Regression validation</a></li> <li><a href="/wiki/Mixed_model" title="Mixed model">Mixed effects models</a></li> <li><a href="/wiki/Simultaneous_equations_model" title="Simultaneous equations model">Simultaneous equations models</a></li> <li><a href="/wiki/Multivariate_adaptive_regression_splines" class="mw-redirect" title="Multivariate adaptive regression splines">Multivariate adaptive regression splines (MARS)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Linear_regression" title="Linear regression">Linear regression</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Simple_linear_regression" title="Simple linear regression">Simple linear regression</a></li> <li><a href="/wiki/Ordinary_least_squares" title="Ordinary least squares">Ordinary least squares</a></li> <li><a href="/wiki/General_linear_model" title="General linear model">General linear model</a></li> <li><a href="/wiki/Bayesian_linear_regression" title="Bayesian linear regression">Bayesian regression</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Non-standard predictors</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonlinear_regression" title="Nonlinear regression">Nonlinear regression</a></li> <li><a href="/wiki/Nonparametric_regression" title="Nonparametric regression">Nonparametric</a></li> <li><a href="/wiki/Semiparametric_regression" title="Semiparametric regression">Semiparametric</a></li> <li><a href="/wiki/Isotonic_regression" title="Isotonic regression">Isotonic</a></li> <li><a href="/wiki/Robust_regression" title="Robust regression">Robust</a></li> <li><a href="/wiki/Heteroscedasticity" class="mw-redirect" title="Heteroscedasticity">Heteroscedasticity</a></li> <li><a href="/wiki/Homoscedasticity" class="mw-redirect" title="Homoscedasticity">Homoscedasticity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Generalized_linear_model" title="Generalized linear model">Generalized linear model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Exponential_family" title="Exponential family">Exponential families</a></li> <li><a href="/wiki/Logistic_regression" title="Logistic regression">Logistic <span style="font-size:85%;">(Bernoulli)</span></a> / <a href="/wiki/Binomial_regression" title="Binomial regression">Binomial</a> / <a href="/wiki/Poisson_regression" title="Poisson regression">Poisson regressions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Partition_of_sums_of_squares" title="Partition of sums of squares">Partition of variance</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analysis_of_variance" title="Analysis of variance">Analysis of variance (ANOVA, anova)</a></li> <li><a href="/wiki/Analysis_of_covariance" title="Analysis of covariance">Analysis of covariance</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Multivariate ANOVA</a></li> <li><a href="/wiki/Degrees_of_freedom_(statistics)" title="Degrees of freedom (statistics)">Degrees of freedom</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Categorical_/_Multivariate_/_Time-series_/_Survival_analysis" style="font-size:114%;margin:0 4em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a> / <a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a> / <a href="/wiki/Time_series" title="Time series">Time-series</a> / <a href="/wiki/Survival_analysis" title="Survival analysis">Survival analysis</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohen%27s_kappa" title="Cohen's kappa">Cohen's kappa</a></li> <li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Graphical_model" title="Graphical model">Graphical model</a></li> <li><a href="/wiki/Poisson_regression" title="Poisson regression">Log-linear model</a></li> <li><a href="/wiki/McNemar%27s_test" title="McNemar's test">McNemar's test</a></li> <li><a href="/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics" title="Cochran–Mantel–Haenszel statistics">Cochran–Mantel–Haenszel statistics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_linear_model" title="General linear model">Regression</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Manova</a></li> <li><a href="/wiki/Principal_component_analysis" title="Principal component analysis">Principal components</a></li> <li><a href="/wiki/Canonical_correlation" title="Canonical correlation">Canonical correlation</a></li> <li><a href="/wiki/Linear_discriminant_analysis" title="Linear discriminant analysis">Discriminant analysis</a></li> <li><a href="/wiki/Cluster_analysis" title="Cluster analysis">Cluster analysis</a></li> <li><a href="/wiki/Statistical_classification" title="Statistical classification">Classification</a></li> <li><a href="/wiki/Structural_equation_modeling" title="Structural equation modeling">Structural equation model</a> <ul><li><a href="/wiki/Factor_analysis" title="Factor analysis">Factor analysis</a></li></ul></li> <li><a href="/wiki/Multivariate_distribution" class="mw-redirect" title="Multivariate distribution">Multivariate distributions</a> <ul><li><a href="/wiki/Elliptical_distribution" title="Elliptical distribution">Elliptical distributions</a> <ul><li><a href="/wiki/Multivariate_normal_distribution" title="Multivariate normal distribution">Normal</a></li></ul></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Time_series" title="Time series">Time-series</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Decomposition_of_time_series" title="Decomposition of time series">Decomposition</a></li> <li><a href="/wiki/Trend_estimation" class="mw-redirect" title="Trend estimation">Trend</a></li> <li><a href="/wiki/Stationary_process" title="Stationary process">Stationarity</a></li> <li><a href="/wiki/Seasonal_adjustment" title="Seasonal adjustment">Seasonal adjustment</a></li> <li><a href="/wiki/Exponential_smoothing" title="Exponential smoothing">Exponential smoothing</a></li> <li><a href="/wiki/Cointegration" title="Cointegration">Cointegration</a></li> <li><a href="/wiki/Structural_break" title="Structural break">Structural break</a></li> <li><a href="/wiki/Granger_causality" title="Granger causality">Granger causality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Specific tests</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dickey%E2%80%93Fuller_test" title="Dickey–Fuller test">Dickey–Fuller</a></li> <li><a href="/wiki/Johansen_test" title="Johansen test">Johansen</a></li> <li><a href="/wiki/Ljung%E2%80%93Box_test" title="Ljung–Box test">Q-statistic <span style="font-size:85%;">(Ljung–Box)</span></a></li> <li><a href="/wiki/Durbin%E2%80%93Watson_statistic" title="Durbin–Watson statistic">Durbin–Watson</a></li> <li><a href="/wiki/Breusch%E2%80%93Godfrey_test" title="Breusch–Godfrey test">Breusch–Godfrey</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Time_domain" title="Time domain">Time domain</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autocorrelation" title="Autocorrelation">Autocorrelation (ACF)</a> <ul><li><a href="/wiki/Partial_autocorrelation_function" title="Partial autocorrelation function">partial (PACF)</a></li></ul></li> <li><a href="/wiki/Cross-correlation" title="Cross-correlation">Cross-correlation (XCF)</a></li> <li><a href="/wiki/Autoregressive%E2%80%93moving-average_model" class="mw-redirect" title="Autoregressive–moving-average model">ARMA model</a></li> <li><a href="/wiki/Box%E2%80%93Jenkins_method" title="Box–Jenkins method">ARIMA model <span style="font-size:85%;">(Box–Jenkins)</span></a></li> <li><a href="/wiki/Autoregressive_conditional_heteroskedasticity" title="Autoregressive conditional heteroskedasticity">Autoregressive conditional heteroskedasticity (ARCH)</a></li> <li><a href="/wiki/Vector_autoregression" title="Vector autoregression">Vector autoregression (VAR)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Frequency_domain" title="Frequency domain">Frequency domain</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Spectral_density_estimation" title="Spectral density estimation">Spectral density estimation</a></li> <li><a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li> <li><a href="/wiki/Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li> <li><a href="/wiki/Wavelet" title="Wavelet">Wavelet</a></li> <li><a href="/wiki/Whittle_likelihood" title="Whittle likelihood">Whittle likelihood</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survival_analysis" title="Survival analysis">Survival</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Survival_function" title="Survival function">Survival function</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kaplan%E2%80%93Meier_estimator" title="Kaplan–Meier estimator">Kaplan–Meier estimator (product limit)</a></li> <li><a href="/wiki/Proportional_hazards_model" title="Proportional hazards model">Proportional hazards models</a></li> <li><a href="/wiki/Accelerated_failure_time_model" title="Accelerated failure time model">Accelerated failure time (AFT) model</a></li> <li><a href="/wiki/First-hitting-time_model" title="First-hitting-time model">First hitting time</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Failure_rate" title="Failure rate">Hazard function</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nelson%E2%80%93Aalen_estimator" title="Nelson–Aalen estimator">Nelson–Aalen estimator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Test</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Log-rank_test" class="mw-redirect" title="Log-rank test">Log-rank test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" 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