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variability</span> </div> </a> <ul id="toc-Methods_used_to_determine_variability-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Discipline within engineering design</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Probabilistic_Design_Distributions.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Probabilistic_Design_Distributions.svg/300px-Probabilistic_Design_Distributions.svg.png" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Probabilistic_Design_Distributions.svg/450px-Probabilistic_Design_Distributions.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Probabilistic_Design_Distributions.svg/600px-Probabilistic_Design_Distributions.svg.png 2x" data-file-width="540" data-file-height="360" /></a><figcaption><a href="/wiki/Statistical_interference" title="Statistical interference">Statistical interference</a> of distributions of applied load and material strength. Load applied and <a href="/wiki/Yield_(engineering)" title="Yield (engineering)">fracture stress</a> are assumed to be normally distributed, and the failure probability is the overlap colored in grey.<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></figcaption></figure> <p><b>Probabilistic design</b> is a discipline within <a href="/wiki/Engineering_design" class="mw-redirect" title="Engineering design">engineering design</a>. It deals primarily with the consideration and minimization of the effects of <a href="/wiki/Random_variable" title="Random variable">random variability</a> upon the performance of an <a href="/wiki/Engineering_system" class="mw-redirect" title="Engineering system">engineering system</a> during the design phase. Typically, these effects studied and optimized are related to quality and reliability. It differs from the classical approach to design by assuming a small probability of failure instead of using the <a href="/wiki/Safety_factor" class="mw-redirect" title="Safety factor">safety factor</a>.<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> Probabilistic design is used in a variety of different applications to assess the likelihood of failure. Disciplines which extensively use probabilistic design principles include product design, <a href="/wiki/Quality_control" title="Quality control">quality control</a>, <a href="/wiki/Systems_engineering" title="Systems engineering">systems engineering</a>, <a href="/wiki/Machine_design" class="mw-redirect" title="Machine design">machine design</a>, <a href="/wiki/Civil_engineering" title="Civil engineering">civil engineering</a> (particularly useful in <a href="/wiki/Limit_state_design" title="Limit state design">limit state design</a>) and manufacturing. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Objective_and_motivations">Objective and motivations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=1" title="Edit section: Objective and motivations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When using a probabilistic approach to design, the designer no longer thinks of each variable as a single value or number. Instead, each variable is viewed as a continuous random variable with a <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a>. From this perspective, probabilistic design predicts the flow of variability (or distributions) through a system.<sup id="cite_ref-:2_4-0" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Because there are so many sources of random and systemic variability when designing materials and structures, it is greatly beneficial for the designer to model the factors studied as random variables. By considering this model, a designer can make adjustments to reduce the flow of random variability, thereby improving engineering quality. Proponents of the probabilistic design approach contend that many quality problems can be predicted and rectified during the early design stages and at a much reduced cost.<sup id="cite_ref-:2_4-1" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><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><p>Typically, the goal of probabilistic design is to identify the design that will exhibit the smallest effects of random variability. Minimizing random variability is essential to probabilistic design because it limits uncontrollable factors, while also providing a much more precise determination of failure probability. This could be the one design option out of several that is found to be most robust. Alternatively, it could be the only design option available, but with the optimum combination of input variables and parameters. This second approach is sometimes referred to as <a href="/wiki/Robustification" title="Robustification">robustification</a>, parameter design or <a href="/wiki/Design_for_Six_Sigma" title="Design for Six Sigma">design for six sigma</a>.<sup id="cite_ref-:2_4-2" class="reference"><a href="#cite_note-:2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Sources_of_variability">Sources of variability</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=2" title="Edit section: Sources of variability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Though the laws of physics dictate the relationships between variables and measurable quantities such as force, <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stress</a>, <a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">strain</a>, and <a href="/wiki/Deflection_(engineering)" title="Deflection (engineering)">deflection</a>, there are still three primary sources of variability when considering these relationships.<sup id="cite_ref-:1_6-0" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The first source of variability is statistical, due to the limitations of having a finite sample size to estimate parameters such as yield stress, <a href="/wiki/Young%27s_modulus" title="Young's modulus">Young's modulus</a>, and <a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">true strain</a>.<sup id="cite_ref-:0_7-0" class="reference"><a href="#cite_note-:0-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Measurement uncertainty is the most easily minimized out of these three sources, as variance is proportional to the inverse of the sample size. </p><p>We can represent variance due to measurement uncertainties as a corrective factor <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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>, which is multiplied by the true mean <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 X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> to yield the measured mean of <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 {\bar {X}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {X}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90b968141b314f4de17f5e63f18dcdc126352bac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.509ex;" alt="{\displaystyle {\bar {X}}}"></span>. Equivalently, <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 {\bar {X}}={\bar {B}}X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {X}}={\bar {B}}X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6b1a3f8f9516b90657d062444f698abade83d5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.822ex; height:2.509ex;" alt="{\displaystyle {\bar {X}}={\bar {B}}X}"></span>. </p><p>This yields the result <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 {\bar {B}}={\frac {\bar {X}}{X}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> <mi>X</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {B}}={\frac {\bar {X}}{X}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/503cfb612c21ed5c4721ae28f09d79c26fcf68bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.679ex; height:5.676ex;" alt="{\displaystyle {\bar {B}}={\frac {\bar {X}}{X}}}"></span> , and the variance of the corrective factor <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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> is given as: </p><p><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 Var[B]={\frac {Var[{\bar {X}}]}{X}}={\frac {Var[X]}{nX}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mo stretchy="false">[</mo> <mi>B</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo stretchy="false">]</mo> </mrow> <mi>X</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>V</mi> <mi>a</mi> <mi>r</mi> <mo stretchy="false">[</mo> <mi>X</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>n</mi> <mi>X</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Var[B]={\frac {Var[{\bar {X}}]}{X}}={\frac {Var[X]}{nX}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/002148471165bf53adabc898af7506dab8705cc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:29.671ex; height:5.843ex;" alt="{\displaystyle Var[B]={\frac {Var[{\bar {X}}]}{X}}={\frac {Var[X]}{nX}}}"></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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> is the correction factor, <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 X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> is the true mean, <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 {\bar {X}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {X}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90b968141b314f4de17f5e63f18dcdc126352bac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.509ex;" alt="{\displaystyle {\bar {X}}}"></span> is the measured mean, 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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> is the number of measurements made.<sup id="cite_ref-:1_6-1" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The second source of variability stems from the inaccuracies and uncertainties of the model used to calculate such parameters. These include the physical models we use to understand loading and their associated effects in materials. The uncertainty from the model of a physical measurable can be determined if both theoretical values according to the model and experimental results are available. </p><p>The measured value <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 {\hat {H}}(\omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}(\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e223240eef5161d7138a5bb0c25cdbd6ba29df0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.319ex; height:3.343ex;" alt="{\displaystyle {\hat {H}}(\omega )}"></span> is equivalent to the theoretical model prediction <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 H(\omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/999e53091c2236d600e49ab5738fbd06abdbe4cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.319ex; height:2.843ex;" alt="{\displaystyle H(\omega )}"></span> multiplied by a model error of <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 \phi (\omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi (\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37c77f9d008f564b2f37074dfbf92befa5ca993e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.641ex; height:2.843ex;" alt="{\displaystyle \phi (\omega )}"></span>, plus the experimental error <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 \varepsilon (\omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ε</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon (\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3db558de8ad5c64c24ffc8214ba8b3e651905c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.339ex; height:2.843ex;" alt="{\displaystyle \varepsilon (\omega )}"></span>.<sup id="cite_ref-:3_8-0" class="reference"><a href="#cite_note-:3-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Equivalently, </p><p><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 {\hat {H}}(\omega )=H(\omega )\phi (\omega )+\varepsilon (\omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>ε</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}(\omega )=H(\omega )\phi (\omega )+\varepsilon (\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ecdea0f4cc1b7fcea3899265a1db82e0f5628296" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.555ex; height:3.343ex;" alt="{\displaystyle {\hat {H}}(\omega )=H(\omega )\phi (\omega )+\varepsilon (\omega )}"></span> </p><p>and the model error takes the general form: </p><p><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 \phi (\omega )=\sum _{i=0}^{n}a_{i}\omega ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>ω</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi (\omega )=\sum _{i=0}^{n}a_{i}\omega ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65329fa321bc8765235bd27572e11e0d9b5ea59a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:16.175ex; height:6.843ex;" alt="{\displaystyle \phi (\omega )=\sum _{i=0}^{n}a_{i}\omega ^{n}}"></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 a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\displaystyle a_{i}}"></span> are coefficients of regression determined from experimental data.<sup id="cite_ref-:3_8-1" class="reference"><a href="#cite_note-:3-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Finally, the last variability source comes from the intrinsic variability of any physical measurable. There is a fundamental random uncertainty associated with all physical phenomena, and it is comparatively the most difficult to minimize this variability. Thus, each physical variable and measurable quantity can be represented as a random variable with a mean and a variability. </p> <div class="mw-heading mw-heading2"><h2 id="Comparison_to_classical_design_principles">Comparison to classical design principles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=3" title="Edit section: Comparison to classical design principles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider the classical approach to performing <a href="/wiki/Tensile_testing" title="Tensile testing">tensile testing</a> in materials. The stress experienced by a material is given as a singular value (i.e., force applied divided by the cross-sectional area perpendicular to the loading axis). The yield stress, which is the maximum stress a material can support before plastic deformation, is also given as a singular value. Under this approach, there is a 0% chance of material failure below the yield stress, and a 100% chance of failure above it. However, these assumptions break down in the real world. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Stress-strain_curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Stress-strain_curve.svg/220px-Stress-strain_curve.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Stress-strain_curve.svg/330px-Stress-strain_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Stress-strain_curve.svg/440px-Stress-strain_curve.svg.png 2x" data-file-width="331" data-file-height="248" /></a><figcaption>The classical stress-strain model for a metal. The material is presumed to fail if stress exceeds the yield stress.</figcaption></figure> <p>The yield stress of a material is often only known to a certain precision, meaning that there is an uncertainty and therefore a probability distribution associated with the known value.<sup id="cite_ref-:1_6-2" class="reference"><a href="#cite_note-:1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:3_8-2" class="reference"><a href="#cite_note-:3-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Let the probability distribution function of the yield strength be given as <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(R)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(R)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/482b1cec7d8f410485628cf860c3b063c3cc9f59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.852ex; height:2.843ex;" alt="{\displaystyle f(R)}"></span>. </p><p>Similarly, the applied load or predicted load can also only be known to a certain precision, and the range of stress which the material will undergo is unknown as well. Let this probability distribution be given as <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(S)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(S)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99a865d36b32ea1d60f15dc3093f5b28093f192b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.587ex; height:2.843ex;" alt="{\displaystyle f(S)}"></span>. </p><p>The probability of failure is equivalent to the area between these two distribution functions, mathematically: </p><p><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 P_{f}=P(R<S)=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }f(R)f(S)dSdR}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <mi>P</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo><</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>S</mi> <mi>d</mi> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{f}=P(R<S)=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }f(R)f(S)dSdR}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9df67578f18fb63eaa483804de9ea7c247fd818d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:40.387ex; height:8.843ex;" alt="{\displaystyle P_{f}=P(R<S)=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }f(R)f(S)dSdR}"></span> </p><p>or equivalently, if we let the difference between yield stress and applied load equal a third function <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 R-S=Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>−</mo> <mi>S</mi> <mo>=</mo> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R-S=Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/074cb26dd8e923a217441f64c63a4c791500d68d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.04ex; height:2.509ex;" alt="{\displaystyle R-S=Q}"></span>, then: </p><p><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 P_{f}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }f(R)f(S)dSdR=\int \limits _{-\infty }^{0}f(Q)dQ}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>S</mi> <mi>d</mi> <mi>R</mi> <mo>=</mo> <munderover> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </munderover> <mi>f</mi> <mo stretchy="false">(</mo> <mi>Q</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{f}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }f(R)f(S)dSdR=\int \limits _{-\infty }^{0}f(Q)dQ}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce7d27dc3d526a5572fd45b4d17a85dc9e00a8b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:41.395ex; height:9.176ex;" alt="{\displaystyle P_{f}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }f(R)f(S)dSdR=\int \limits _{-\infty }^{0}f(Q)dQ}"></span> </p><p>where the <a href="/wiki/Variance" title="Variance">variance</a> of the mean difference <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 Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> is given by <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 \sigma _{Q}^{2}={\sqrt {\sigma _{R}^{2}+\sigma _{S}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{Q}^{2}={\sqrt {\sigma _{R}^{2}+\sigma _{S}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/559e29379b3aab81d8b14778a48a9ca3c26e9aa1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.549ex; height:4.843ex;" alt="{\displaystyle \sigma _{Q}^{2}={\sqrt {\sigma _{R}^{2}+\sigma _{S}^{2}}}}"></span> . </p><p>The probabilistic design principles allow for precise determination of failure probability, whereas the classical model assumes absolutely no failure before yield strength.<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> It is clear that the classical applied load vs. yield stress model has limitations, so modeling these variables with a probability distribution to calculate failure probability is a more precise approach. The probabilistic design approach allows for the determination of material failure under all loading conditions, associating quantitative probabilities to failure chance in place of a definitive yes or no. </p> <div class="mw-heading mw-heading2"><h2 id="Methods_used_to_determine_variability">Methods used to determine variability</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=4" title="Edit section: Methods used to determine variability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Poutre2S22.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Poutre2S22.jpg/220px-Poutre2S22.jpg" decoding="async" width="220" height="136" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Poutre2S22.jpg/330px-Poutre2S22.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Poutre2S22.jpg/440px-Poutre2S22.jpg 2x" data-file-width="855" data-file-height="529" /></a><figcaption>Finite element analysis (pictured here, of a dogbone under uniaxial stress) is a primary method used to provide theoretical values for stress and failure in probabilistic design.<sup id="cite_ref-:4_10-0" class="reference"><a href="#cite_note-:4-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>In essence, probabilistic design focuses upon the prediction of the effects of variability. In order to be able to predict and calculate variability associated with model uncertainty, many methods have been devised and utilized across different disciplines to determine theoretical values for parameters such as stress and strain. Examples of theoretical models used alongside probabilistic design include: </p> <ul><li><a href="/wiki/Finite_element_method" title="Finite element method">Finite element analysis</a><sup id="cite_ref-:4_10-1" class="reference"><a href="#cite_note-:4-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Stochastic_process" title="Stochastic process">Stochastic</a> finite element method<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></li> <li><a href="/wiki/Boundary_element_method" title="Boundary element method">Boundary element method</a></li> <li><a href="/wiki/Meshfree_methods" title="Meshfree methods">Meshfree methods</a></li> <li>Analytical methods (refer to classical design principles)</li></ul> <p>Additionally, there are many statistical methods used to quantify and predict the random variability in the desired measurable. Some methods that are used to predict the random variability of an output include: </p> <ul><li>the <a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo method</a> (including <a href="/wiki/Latin_hypercube_sampling" title="Latin hypercube sampling">Latin hypercubes</a>);<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></li> <li><a href="/wiki/Propagation_of_error" class="mw-redirect" title="Propagation of error">propagation of error</a>;</li> <li><a href="/wiki/Design_of_experiments" title="Design of experiments">design of experiments</a> (DOE)</li> <li><a href="/wiki/Method_of_moments_(statistics)" title="Method of moments (statistics)">the method of moments</a></li> <li><a href="/wiki/Statistical_interference" title="Statistical interference">Statistical interference</a></li> <li><a href="/wiki/Quality_function_deployment" title="Quality function deployment">quality function deployment</a></li> <li><a href="/wiki/Failure_mode_and_effects_analysis" title="Failure mode and effects analysis">Failure mode and effects analysis</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Interval_finite_element" title="Interval finite element">Interval finite element</a></li> <li><a href="/wiki/Stochastic_modelling_(insurance)" title="Stochastic modelling (insurance)">Stochastic modeling</a></li> <li><a href="/wiki/First-order_second-moment_method" title="First-order second-moment method">First-order second-moment method</a></li> <li><a href="/wiki/Weibull_distribution" title="Weibull distribution">Weibull distribution</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=6" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><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 id="CITEREFSundarthWoeste,_Frank_E.;_Galligan,_William1978" class="citation cs2 cs1-prop-long-vol">Sundarth, S; 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(2013-12-01). <a rel="nofollow" class="external text" href="https://go.gale.com/ps/i.do?p=AONE&sw=w&issn=13923730&v=2.1&it=r&id=GALE%7CA368581850&sid=googleScholar&linkaccess=abs">"A method for linking safety factor to the target probability of failure in fire safety engineering"</a>. <i>Journal of Civil Engineering and Management</i>. <b>19</b> (S1): S212–S212. <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/10.3846%2F13923730.2013.802718">10.3846/13923730.2013.802718</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Civil+Engineering+and+Management&rft.atitle=A+method+for+linking+safety+factor+to+the+target+probability+of+failure+in+fire+safety+engineering&rft.volume=19&rft.issue=S1&rft.pages=S212-S212&rft.date=2013-12-01&rft_id=info%3Adoi%2F10.3846%2F13923730.2013.802718&rft.aulast=Kong&rft.aufirst=Depeng&rft.au=Lu%2C+Shouxiang&rft.au=Frantzich%2C+Hakan&rft.au=Lo%2C+S.+M.&rft_id=https%3A%2F%2Fgo.gale.com%2Fps%2Fi.do%3Fp%3DAONE%26sw%3Dw%26issn%3D13923730%26v%3D2.1%26it%3Dr%26id%3DGALE%257CA368581850%26sid%3DgoogleScholar%26linkaccess%3Dabs&rfr_id=info%3Asid%2Fen.wikipedia.org%3AProbabilistic+design" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Ang and Tang (2006) <i>Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering.</i> John Wiley & Sons. <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/0-471-72064-X" title="Special:BookSources/0-471-72064-X">0-471-72064-X</a></li> <li>Ash (1993) <i>The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists</i> (<i>and Everyone Else</i>). Wiley-IEEE 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/0-7803-1051-9" title="Special:BookSources/0-7803-1051-9">0-7803-1051-9</a></li> <li>Clausing (1994) <i>Total Quality Development: A Step-By-Step Guide to World-Class Concurrent Engineering.</i> American Society of Mechanical Engineers. <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/0-7918-0035-0" title="Special:BookSources/0-7918-0035-0">0-7918-0035-0</a></li> <li>Haugen (1980) <i>Probabilistic mechanical design.</i> Wiley. <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/0-471-05847-5" title="Special:BookSources/0-471-05847-5">0-471-05847-5</a></li> <li>Papoulis (2002) <i>Probability, Random Variables and Stochastic Process.</i> McGraw-Hill Publishing Co. <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/0-07-119981-0" title="Special:BookSources/0-07-119981-0">0-07-119981-0</a></li> <li>Siddall (1982) <i>Optimal Engineering 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/0-8247-1633-7" title="Special:BookSources/0-8247-1633-7">0-8247-1633-7</a></li> <li>Dodson, B., Hammett, P., and Klerx, R. (2014) <i>Probabilistic Design for Optimization and Robustness for Engineers</i> John Wiley & Sons, Inc. <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/978-1-118-79619-1" title="Special:BookSources/978-1-118-79619-1">978-1-118-79619-1</a></li> <li>Cederbaum G., Elishakoff I., Aboudi J. and Librescu L., Random Vibration and Reliability of Composite Structures, Technomic, Lancaster, 1992, XIII + pp. 191; <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%2B87762%2B865%2B3" title="Special:BookSources/0+87762+865+3">0 87762 865 3</a></li> <li>Elishakoff I., Lin Y.K. and Zhu L.P., Probabilistic and Convex Modeling of Acoustically Excited Structures, Elsevier Science Publishers, Amsterdam, 1994, VIII + pp. 296; <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%2B444%2B81624%2B0" title="Special:BookSources/0+444+81624+0">0 444 81624 0</a></li> <li>Elishakoff I., Probabilistic Methods in the Theory of Structures: Random Strength of Materials, Random Vibration, and Buckling, World Scientific, Singapore, <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/978-981-3149-84-7" title="Special:BookSources/978-981-3149-84-7">978-981-3149-84-7</a>, 2017</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Probabilistic_design&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://grassmannalgebra.info/probabilisticdesign">Probabilistic design</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160820042215/http://www.ndaportal.com/non-deterministic-approaches-handbook.html">Non Deterministic Approaches in Engineering</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 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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 class="mw-selflink selflink">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 href="/wiki/Reliability_engineering" title="Reliability engineering">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 expanded 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" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible uncollapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Applications" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_fields_of_application_of_statistics" title="List of fields of application of statistics">Applications</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/Biostatistics" title="Biostatistics">Biostatistics</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/Bioinformatics" title="Bioinformatics">Bioinformatics</a></li> <li><a href="/wiki/Clinical_trial" title="Clinical trial">Clinical trials</a> / <a href="/wiki/Clinical_study_design" title="Clinical study design">studies</a></li> <li><a href="/wiki/Epidemiology" title="Epidemiology">Epidemiology</a></li> <li><a href="/wiki/Medical_statistics" title="Medical statistics">Medical statistics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Engineering_statistics" title="Engineering statistics">Engineering statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div 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