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.inner[data-v-e6aca418]{max-width:68em;margin:0 auto}}.title[data-v-e6aca418]{font-family:'Relative Faux', sans-serif;font-weight:400;font-style:normal;-webkit-font-smoothing:auto;-webkit-text-size-adjust:none;color:#fffdea;font-size:1.4em;line-height:1.3;display:block;margin-bottom:1.5rem}.title[data-v-e6aca418]:hover{text-decoration:underline}.link[data-v-e6aca418]{font-family:'Relative Faux', sans-serif;font-weight:400;font-style:normal;-webkit-font-smoothing:auto;-webkit-text-size-adjust:none;color:#fffdea;font-size:1.4em;line-height:1.6;display:block;margin-bottom:1.5rem}.link[data-v-e6aca418]:hover{text-decoration:underline}.icr[data-v-e6aca418]{display:inline-block;font-size:2em;left:0;margin-right:0.5rem;text-indent:initial}.icr[data-v-e6aca418]:last-child{margin-right:0}.icr img[data-v-e6aca418]{width:60%}.meta[data-v-e6aca418],.address[data-v-e6aca418]{font-family:'Relative Faux', 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data-v-56230ffb>Open Access is an initiative that aims to make scientific research freely available to all. To date our community has made over 100 million downloads. It’s based on principles of collaboration, unobstructed discovery, and, most importantly, scientific progression. As PhD students, we found it difficult to access the research we needed, so we decided to create a new Open Access publisher that levels the playing field for scientists across the world. How? By making research easy to access, and puts the academic needs of the researchers before the business interests of publishers.</p></div> <div class="drop-box" data-v-56230ffb><a href="/authors-and-editors" class="drop-item" data-v-56230ffb>Our Authors and Editors</a> <p data-v-56230ffb>We are a community of more than 103,000 authors and editors from 3,291 institutions spanning 160 countries, including Nobel Prize winners and some of the world’s most-cited researchers. Publishing on IntechOpen allows authors to earn citations and find new collaborators, meaning more people see your work not only from your own field of study, but from other related fields too.</p></div> <div class="drop-box" data-v-56230ffb><a href="/page/content-alerts" class="drop-item" data-v-56230ffb>Content Alerts</a> <p data-v-56230ffb>Brief introduction to this section that descibes Open Access especially from an IntechOpen perspective</p> <a href="/how-open-access-publishing-with-intechopen-works" class="nav-item" data-v-56230ffb>How it Works</a> <a href="#" class="nav-item" data-v-56230ffb>Manage preferences</a></div> <div class="drop-box" data-v-56230ffb><a href="/page/contact-us" class="drop-item" data-v-56230ffb>Contact</a> <p data-v-56230ffb>Want to get in touch? Contact our London head office or <a href="#" data-v-56230ffb>media team here</a></p> <a href="/page/careers-at-intechopen" class="drop-item" data-v-56230ffb>Careers</a> <p data-v-56230ffb>Our team is growing all the time, so we’re always on the lookout for smart people who want to help us reshape the world of scientific publishing.</p></div></div></div></div></header> <section data-v-54f135f0 data-v-7969e618><div class="privacy-policy" data-v-54f135f0><h1 class="title" data-v-54f135f0>Privacy Policy</h1> <p data-v-54f135f0>This privacy policy applies to <a href="https://www.intechopen.com" data-v-54f135f0>www.intechopen.com</a> owned and operated by IntechOpen (hereafter referred to as “IntechOpen”, "We", "Us", or “Our”). This Policy sets out how IntechOpen uses and protects any information that you, the ("user") give when you use this website. IntechOpen is committed to ensuring that your privacy is protected at all times. Should we ask you to provide certain information by which you can be identified when using this website, you can be assured that such information will only be used in strictest accordance with this Privacy Policy.</p> <p data-v-54f135f0>IntechOpen does not sell, rent, or otherwise provide your personal information to third parties unless they are publicly available as part of the publishing activities, or we have your permission, or are required by law to do so. IntechOpen may change this Policy from time to time by updating this page. You are invited to check this page to ensure that you agree with the changes.</p> <p data-v-54f135f0>1. WHO ARE WE?</p> <p data-v-54f135f0>We are IntechOpen, the world's leading publisher of Open Access books. INTECHOPEN LIMITED is a privately owned company registered in England and Wales, No. 11086078 Registered Office: 167-169 Great Portland Street, London, W1W 5PF, UNITED KINGDOM.</p> <p data-v-54f135f0>2. USAGE OF INFORMATION</p> <p data-v-54f135f0>Registration on the IntechOpen web page is for Authors, prospective Editors and other users who wish to send suggestions. Involvement is entirely optional and voluntary. We use the information you provide to:</p> <ul class="list" data-v-54f135f0><li data-v-54f135f0>Allow IntechOpen to send service email notifications or promotional messages about new publications released.</li> <li data-v-54f135f0>Administer your account and customize the service we provide to you and other users</li> <li data-v-54f135f0>Provide you with any material you requested (as a download or a print version)</li> <li data-v-54f135f0>Respond to any request or question you may have and in other cases when we have legitimate interests to process your personal data</li> <li data-v-54f135f0>Fulfil any our legal obligation (when applicable).</li></ul> <p data-v-54f135f0>3. WHAT WE COLLECT</p> <p data-v-54f135f0>For the purposes stated above we may collect the following information:</p> <ul class="list" data-v-54f135f0><li data-v-54f135f0>First name, last name, academic/job title, organization/institution and previous publications</li> <li data-v-54f135f0>Contact information in the form of an email address, postal address and country of residence</li> <li data-v-54f135f0>Other information regarding your scientific field of interest, education and work experience</li> <li data-v-54f135f0>Password</li></ul> <p data-v-54f135f0>4. ADDITIONAL INFORMATION COLLECTED</p> <p data-v-54f135f0>In order to deliver a better service, IntechOpen tracks patterns of use on this site. We note which links are clicked on to determine what areas, chapters, and books are of interest to our visitors. As with all websites, we automatically receive from Internet usage, information such as your IP address, browser type, internet service provider (ISP), referring/exit pages, operating system, date/time stamp, and/or clickstream data, your mobile provider and your mobile device. We store all data in log files. We use cookies and other technologies to recognize you, study traffic patterns on our website, and customize your experience.</p> <p data-v-54f135f0>You can choose to accept or decline cookies. Most web browsers automatically accept cookies, but you can usually modify your browser setting to decline cookies if you prefer. This may prevent you from taking full advantage of the website.</p> <p data-v-54f135f0>5. YOUR RIGHTS</p> <p data-v-54f135f0>Authors, Co-authors, Editors and Co-editors can choose what information to make available to other users.</p> <p data-v-54f135f0>With the exception of your e-mail address (which works as a login), you are free to change your personal information at any time. IntechOpen will provide you with information about whether we hold any of your personal information. If your personal information changes, you may correct, update, or delete it by making changes through your User Panel, or by contacting us by post at the address given in the contact information listed below.</p> <p data-v-54f135f0>You can submit a request to close your IntechOpen account at any time. If you no longer desire our services, you can deactivate your account by emailing us at <a href="mailto:info@intechopen.com" data-v-54f135f0>info@intechopen.com</a> or by contacting us by postal mail using the contact information listed below. We will respond to your request within a reasonable timeframe.</p> <p data-v-54f135f0>6. OPEN ACCESS</p> <p data-v-54f135f0>IntechOpen is an Open Access publisher. All published Work will be permanently and freely available on our webpage. Certain personal information such as first name, last name, affiliation and email address shall be publicly visible and available along with the published Work. It is the basis of Open Access to freely share all scientific Works and information associated with those Works.</p> <p data-v-54f135f0>7. THIRD PARTIES</p> <p data-v-54f135f0>IntechOpen does not sell, rent, or otherwise provide your personal information to third parties unless we have your permission or are required by law so as to comply with a subpoena or similar legal process. </p> <p data-v-54f135f0>Please note that in order to deliver certain services (for example, Chapter publication, processing payments, billing services, postal services etc.), we may share information with third parties as well as with our affiliates (the latter acting as our sub-processors).</p> <p data-v-54f135f0>To process payments made by you, we share some of your information with the payment processing company we use. In the case of delivery of hard copies of books to Authors, or other parties ordering such publications, we share with third parties conducting postal delivery services the information required in order to carry out the delivery. These companies are authorized to use your personal information only as necessary to provide these services to us.</p> <p data-v-54f135f0>Billing services are provided by our EU affiliates as well as maintenance and other services supporting our daily activities, in which cases they may have access to your personal data. In these situations, IntechOpen remains the data controller and our EU affiliates act in line with our instructions as our subprocessors. </p> <p data-v-54f135f0>8. E-MAIL POLICY</p> <p data-v-54f135f0>IntechOpen may send you service communications by email. If you have previously agreed to us using your personal information for email/newsletter services, IntechOpen may send information which you might find of interest. You may change your mind and unsubscribe at any time by emailing us at <a href="mailto:info@intechopen.com" data-v-54f135f0>info@intechopen.com</a>. Additionally, you can unsubscribe by clicking the Unsubscribe button in all our marketing emails.</p> <p data-v-54f135f0>9. SECURITY OF YOUR PERSONAL INFORMATION</p> <p data-v-54f135f0>When you give us personal information, we take steps to ensure that it is treated securely. Any sensitive information is encrypted and protected.</p> <p data-v-54f135f0>Once we receive your information, we will take all necessary precautions to ensure its security in our systems. You will need to use a password to access certain parts of our website and it is your sole responsibility to keep your password confidential. We ask you not to share your password with anyone.</p> <p data-v-54f135f0>10. TRANSFERRING YOUR INFORMATION OUTSIDE OF EUROPE</p> <p data-v-54f135f0>As part of the services offered to you through this website, the information which you provide to us may be transferred to countries outside the UK and the European Union (“EU”). By way of example, this may happen if any of our servers are from time to time located in a country outside of the EU. These countries may not have similar data protection laws to the UK. If we transfer your information outside of the EU in this way, we will take steps to ensure that appropriate security measures are taken with the aim of ensuring that your privacy rights continue to be protected as outlined in this Privacy Policy.</p> <p data-v-54f135f0>11. CUSTOMER TESTIMONIALS / COMMENTS / REVIEWS</p> <p data-v-54f135f0>In the Author Acknowledgments section of our website we post Customer testimonials/comments/reviews. These may contain personal information. Testimonials are stored in a database held within IntechOpen. Prior to posting a testimonial, we obtain the Customer's consent to posting his or her name along with the testimonial. If you wish to update or delete your testimonial, please contact us at <a href="mailto:info@intechopen.com" data-v-54f135f0>info@intechopen.com</a>.</p> <p data-v-54f135f0>12. COOKIES & OTHER TRACKING TECHNOLOGIES</p> <p data-v-54f135f0>Technologies such as cookies, or similar technologies, are used by IntechOpen and our business partners, affiliates, analytics or service providers. These technologies are used in analyzing trends, administering the site, tracking users’ movements around the site and in gathering demographic information about our user base as a whole. We may receive reports based on the use of these technologies from these companies on an individual, as well as an aggregated basis.</p> <p data-v-54f135f0>We use cookies for user authentication. Users can control the use of cookies at the individual browser level. If you reject cookies, you may still use our site, but your ability to use some features or areas of our site may be limited.</p> <p data-v-54f135f0>For more information about how we use cookies and your choices, please review our <a href="/cookie-policy" data-v-54f135f0> Cookie Policy</a></p> <p data-v-54f135f0>If you have any questions about the use of cookies on our website please e-mail us at <a href="mailto:info@intechopen.com" data-v-54f135f0>info@intechopen.com</a>. We partner with a third party to either display advertising on our website or to manage our advertising on other sites. Our third party partner may use cookies, or similar technologies, in order to provide you advertising based upon your browsing activities and interests. If you wish to opt out of interest-based advertising, click <a href="mailto:info@intechopen.com" data-v-54f135f0>info@intechopen.com</a>. </p> <p data-v-54f135f0>Please note you will continue to receive generic ads.</p> <p data-v-54f135f0>13. SECURITY</p> <p data-v-54f135f0>We follow generally accepted standards to protect the personal information submitted to us, both during transmission and once it is received. If you have any questions about the security of your personal information, you can contact us at <a href="mailto:info@intechopen.com" data-v-54f135f0>info@intechopen.com</a>.</p> <p data-v-54f135f0>We are committed to ensuring that your information is secure. In order to prevent unauthorized access or disclosure, we have put in place suitable physical, electronic, and managerial procedures to safeguard and secure the information we collect online. However, given that the Internet is not a secure medium, there is no guarantee that information may not be accessed, disclosed, altered, or destroyed by a breach of any of our physical, technical, or managerial safeguards. 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Book Series are headed by Series Editors, and a team of Topic Editors supported by international Editorial Board members. Topics are \u003Cstrong\u003Ealways open for submissions\u003C\u002Fstrong\u003E, with an Annual Volume published each calendar year.\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EAfter a robust peer-review process, accepted works are published quickly, thanks to \u003Cstrong\u003EOnline First\u003C\u002Fstrong\u003E, ensuring research is made available to the scientific community without delay.\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EOur innovative Book Series format brings you:\u003C\u002Fp\u003E\\n\\n\u003Cul\u003E\\n\\t\u003Cli\u003E\u003Cstrong\u003ETopic Focused Publications\u003C\u002Fstrong\u003E - Each topic showcases high impact subject \u003Cstrong\u003Eareas\u003C\u002Fstrong\u003E\u003C\u002Fli\u003E\\n\\t\u003Cli\u003E\u003Cstrong\u003ERenowned Editorial Expertise\u003C\u002Fstrong\u003E - Series Editors, Topic Editors, and a team of international Board Members that permanently support each Book Series\u003C\u002Fli\u003E\\n\\t\u003Cli\u003E\u003Cstrong\u003EFast Publishing\u003C\u002Fstrong\u003E - quick turnaround which is unique for book publishing\u003C\u002Fli\u003E\\n\\t\u003Cli\u003EThe benefit of \u003Cstrong\u003EISSN and ISBN\u003C\u002Fstrong\u003E for increased citation and indexing possibilities\u003C\u002Fli\u003E\\n\u003C\u002Ful\u003E\\n\\n\u003Cp\u003E\u003Cvideo controls style=\\\"width: 100%;-webkit-box-shadow: 0px 0px 2px 0px rgba(0, 0, 0, 0.05);box-shadow: 2px -2px 6px 2px rgb(0 0 0 \u002F 7%);\\\"\u003E\u003Csource src=\\\"https:\u002F\u002Fcdn.intechopen.com\u002Fpublic\u002Fvideos\u002FSeriesLaunch.mp4\\\" type=\\\"video\u002Fmp4\\\"\u002F\u003E\u003C\u002Fvideo\u003E\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EIntechOpen Book Series will also publish a program of research-driven Thematic Edited Volumes that focus on specific areas and allow for a more in-depth overview of a particular subject.\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EIntechOpen Book Series will be launching regularly to offer our authors and editors exciting opportunities to publish their research Open Access. We will begin by relaunching some of our existing Book Series in this innovative book format, and will expand in 2022 into rapidly growing research fields that are driving and advancing society. \u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Cstrong\u003ELaunching 2021\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Ca href=\\\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F14\u002F\\\" target=\\\"_blank\\\"\u003EArtificial Intelligence\u003C\u002Fa\u003E, ISSN 2633-1403\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Ca href=\\\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F13\u002F\\\" target=\\\"_blank\\\"\u003EVeterinary Medicine and Science\u003C\u002Fa\u003E, ISSN 2632-0517\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Ca href=\\\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F11\u002F\\\" target=\\\"_blank\\\"\u003EBiochemistry\u003C\u002Fa\u003E, ISSN 2632-0983\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Ca href=\\\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F7\u002F\\\" target=\\\"_blank\\\"\u003EBiomedical Engineering\u003C\u002Fa\u003E, ISSN 2631-5343\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Ca href=\\\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F6\u002F\\\" target=\\\"_blank\\\"\u003EInfectious Diseases\u003C\u002Fa\u003E, ISSN 2631-6188\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EPhysiology (Coming Soon)\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EDentistry (Coming Soon)\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EWe invite you to explore our \u003Ca href=\\\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\\\" target=\\\"_blank\\\"\u003EIntechOpen Book Series\u003C\u002Fa\u003E, find the right publishing program for you and reach your desired audience in record time. \u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Cem\u003ENote: Edited in October 2021\u003C\u002Fem\u003E\u003C\u002Fp\u003E\\n\"}]","published":true,"mainMedia":{"caption":"","originalUrl":"\u002Fmedia\u002Foriginal\u002F132"}},"components":[{"type":"htmlEditorComponent","content":"\u003Cp\u003EWith the desire to make book publishing more relevant for the digital age and offer innovative Open Access publishing options, we are thrilled to announce the launch of our new publishing format: \u003Ca href=\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\" target=\"_blank\"\u003EIntechOpen Book Series\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\n\n\u003Cp\u003EDesigned to cover fast-moving research fields in rapidly expanding areas, our Book Series feature a Topic structure allowing us to present the most relevant sub-disciplines. Book Series are headed by Series Editors, and a team of Topic Editors supported by international Editorial Board members. Topics are \u003Cstrong\u003Ealways open for submissions\u003C\u002Fstrong\u003E, with an Annual Volume published each calendar year.\u003C\u002Fp\u003E\n\n\u003Cp\u003EAfter a robust peer-review process, accepted works are published quickly, thanks to \u003Cstrong\u003EOnline First\u003C\u002Fstrong\u003E, ensuring research is made available to the scientific community without delay.\u003C\u002Fp\u003E\n\n\u003Cp\u003EOur innovative Book Series format brings you:\u003C\u002Fp\u003E\n\n\u003Cul\u003E\n\t\u003Cli\u003E\u003Cstrong\u003ETopic Focused Publications\u003C\u002Fstrong\u003E - Each topic showcases high impact subject \u003Cstrong\u003Eareas\u003C\u002Fstrong\u003E\u003C\u002Fli\u003E\n\t\u003Cli\u003E\u003Cstrong\u003ERenowned Editorial Expertise\u003C\u002Fstrong\u003E - Series Editors, Topic Editors, and a team of international Board Members that permanently support each Book Series\u003C\u002Fli\u003E\n\t\u003Cli\u003E\u003Cstrong\u003EFast Publishing\u003C\u002Fstrong\u003E - quick turnaround which is unique for book publishing\u003C\u002Fli\u003E\n\t\u003Cli\u003EThe benefit of \u003Cstrong\u003EISSN and ISBN\u003C\u002Fstrong\u003E for increased citation and indexing possibilities\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp\u003E\u003Cvideo controls style=\"width: 100%;-webkit-box-shadow: 0px 0px 2px 0px rgba(0, 0, 0, 0.05);box-shadow: 2px -2px 6px 2px rgb(0 0 0 \u002F 7%);\"\u003E\u003Csource src=\"https:\u002F\u002Fcdn.intechopen.com\u002Fpublic\u002Fvideos\u002FSeriesLaunch.mp4\" type=\"video\u002Fmp4\"\u002F\u003E\u003C\u002Fvideo\u003E\u003C\u002Fp\u003E\n\n\u003Cp\u003EIntechOpen Book Series will also publish a program of research-driven Thematic Edited Volumes that focus on specific areas and allow for a more in-depth overview of a particular subject.\u003C\u002Fp\u003E\n\n\u003Cp\u003EIntechOpen Book Series will be launching regularly to offer our authors and editors exciting opportunities to publish their research Open Access. We will begin by relaunching some of our existing Book Series in this innovative book format, and will expand in 2022 into rapidly growing research fields that are driving and advancing society. \u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Cstrong\u003ELaunching 2021\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Ca href=\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F14\u002F\" target=\"_blank\"\u003EArtificial Intelligence\u003C\u002Fa\u003E, ISSN 2633-1403\u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Ca href=\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F13\u002F\" target=\"_blank\"\u003EVeterinary Medicine and Science\u003C\u002Fa\u003E, ISSN 2632-0517\u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Ca href=\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F11\u002F\" target=\"_blank\"\u003EBiochemistry\u003C\u002Fa\u003E, ISSN 2632-0983\u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Ca href=\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F7\u002F\" target=\"_blank\"\u003EBiomedical Engineering\u003C\u002Fa\u003E, ISSN 2631-5343\u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Ca href=\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\u002F6\u002F\" target=\"_blank\"\u003EInfectious Diseases\u003C\u002Fa\u003E, ISSN 2631-6188\u003C\u002Fp\u003E\n\n\u003Cp\u003EPhysiology (Coming Soon)\u003C\u002Fp\u003E\n\n\u003Cp\u003EDentistry (Coming Soon)\u003C\u002Fp\u003E\n\n\u003Cp\u003EWe invite you to explore our \u003Ca href=\"https:\u002F\u002Fwww.intechopen.com\u002Fseries\" target=\"_blank\"\u003EIntechOpen Book Series\u003C\u002Fa\u003E, find the right publishing program for you and reach your desired audience in record time. \u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Cem\u003ENote: Edited in October 2021\u003C\u002Fem\u003E\u003C\u002Fp\u003E\n"}],"latestNews":[{"slug":"green-energy-and-environmental-technology-journal-supporting-the-un-sustainable-development-goals-20241105","title":"Green Energy and Environmental Technology Journal: Supporting the UN Sustainable Development Goals"},{"slug":"intechopen-signs-research4life-publishers-recommitment-20241029","title":"IntechOpen Signs Research4Life Publishers Recommitment"},{"slug":"intechopen-launches-open-science-hub-20241028","title":"IntechOpen Launches Open Science Hub"},{"slug":"2024-best-paper-award-from-the-ai-computer-science-and-robotics-technology-journal-20241004","title":"2024 Best Paper Award From the AI, Computer Science, and Robotics Technology Journal"},{"slug":"peer-review-week-2024-spotlight-an-interview-with-global-campus-co-founder-paul-tuinenburg-20240927","title":"Peer Review Week Spotlight: An Interview with Global Campus Co-Founder Paul Tuinenburg"},{"slug":"new-open-access-books-from-the-knowledge-unlatched-select-programme-2024-20240819","title":"New Open Access Books from the Knowledge Unlatched Select Programme 2024"},{"slug":"intechopen-presents-interviews-for-young-scientists-with-science-s-leading-minds-20240708","title":"IntechOpen Presents Interviews for Young Scientists with Science's Leading Minds"},{"slug":"recent-intechopen-book-series-launches-20240705","title":"Recent IntechOpen Book Series Launches"}]},"book":{"item":{"type":"book","id":"1002668","leadTitle":null,"fullTitle":"New Insights on Cerebrospinal Fluid","title":"New Insights on Cerebrospinal Fluid","subtitle":null,"reviewType":"peer-reviewed","abstract":"Cerebrospinal fluid as a diagnostic tool has widened its reach in clinical practice due to recent advances in liquid biopsy technology and molecular diagnostic techniques. Nowadays, the widespread use of molecular biology in clinical practice shapes our decision-making processes and prognostic course at the bedside. In this book, we cover recent advances in cerebrospinal fluid analysis options and how these changes have shaped and will change our daily clinical practice. Future technology is coming rapidly, and these changes are helping humanity to be more precise and rapid in treating cerebrospinal fluid-related pathologies. I hope you will find some of your answers in this book about recent advances in cerebrospinal fluid as a diagnostic and prognostic tool.","isbn":"978-0-85466-505-1","printIsbn":"978-0-85466-506-8","pdfIsbn":"978-0-85466-507-5","doi":"10.5772\u002Fintechopen.1000434","price":100,"priceEur":null,"priceUsd":null,"priceCbs":null,"slug":null,"numberOfPages":66,"isOpenForSubmission":true,"isInWos":null,"isInBkci":false,"hash":"111b8ea1417aef825968da47b3aeebc7","bookSignature":"Pinar Kuru Bektasoglu","publishedDate":"November 20th 2024","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F12589.jpg","cdnWebCoverURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1002668\u002F1731396822-620480333\u002Fweb-cover.jpg","cdnWebCoverURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1002668\u002F1731396822-620480333\u002Fweb-cover-300.jpg","numberOfDownloads":87,"numberOfViews":null,"numberOfWosCitations":null,"numberOfCrossrefCitations":0,"numberOfCrossrefCitationsByBook":0,"numberOfDimensionsCitations":0,"numberOfDimensionsCitationsByBook":null,"hasAltmetrics":0,"totalAltmetricsMentions":0,"numberOfTotalCitations":0,"isAvailableForWebshopOrdering":true,"dateEndFirstStepPublish":"October 13th 2023","dateEndSecondStepPublish":"December 8th 2023","dateEndThirdStepPublish":"January 12th 2024","dateEndFourthStepPublish":"April 1st 2024","dateEndFifthStepPublish":"May 31st 2024","currentStepOfPublishingProcess":5,"indexedIn":"1,2,3,4,5,6","editedByType":null,"kuFlag":false,"sdgRelated":false,"featuredMarkup":null,"isPublished":true,"isPublisherCbs":false,"noAds":0,"editors":[{"id":"244230","title":"Dr.","name":"Pinar","middleName":null,"surname":"Kuru Bektasoglu","slug":"pinar-kuru-bektasoglu","fullName":"Pinar Kuru Bektasoglu","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F244230\u002F1731414997\u002Fprofile\u002Fimage1.jpg","biography":"Dr. Pinar Kuru Bektaşoğlu is working as a neurosurgery consultant at Istanbul Fatih Sultan Mehmet Education and Research Hospital. She graduated from Marmara University School of Medicine, Turkey, in 2014. She completed her neurosurgical residency in 2021 and her Ph.D. in physiology at Marmara University Institute of Health Sciences, also in 2021. She worked as a research fellow in the Department of Neurological Surgery at Yeditepe University, Turkiye, for six months studying white matter fiber dissection. She has given more than 80 presentations at international and national meetings and published 50 papers in peer-reviewed journals. She also edited four books and wrote 11 book chapters. She has a keen interest in neurovascular and neuro-oncological surgeries and translational neuroscience.","institutionString":"Istanbul Fatih Sultan Mehmet Education and Research Hospital","position":null,"outsideEditionCount":null,"totalCites":0,"totalAuthoredChapters":"3","totalChapterViews":"0","totalEditedBooks":"4","institution":null,"countryString":"Turkey"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null,"coeditorOne":null,"coeditorTwo":null,"coeditorThree":null,"coeditorFour":null,"coeditorFive":null,"topics":[{"id":"213","title":"Neurobiology","slug":"life-sciences-neuroscience-neurobiology"}],"productType":{"id":"1","title":"Edited Volume","chapterContentType":"chapter","authoredCaption":"Edited by"},"subseries":null,"tags":null,"_preview":0,"chapters":[{"id":"1207500","title":"Introductory Chapter: New Insights on Cerebrospinal Fluid","doi":"10.5772\u002Fintechopen.1007032","slug":null,"totalDownloads":20,"totalCrossrefCites":0,"totalDimensionsCites":0,"hasAltmetrics":0,"orderNumber":1,"abstract":"\n","signatures":"Pinar Kuru Bektasoglu","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F1207500","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F1207500","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"244230","title":"Dr.","name":"Pinar","surname":"Kuru Bektasoglu","slug":"pinar-kuru-bektasoglu","fullName":"Pinar Kuru Bektasoglu"}],"corrections":null,"_preview":0},{"id":"1167866","title":"Hydrocephalus: A Review of Etiology Driven Treatment Strategies","doi":"10.5772\u002Fintechopen.1003972","slug":null,"totalDownloads":9,"totalCrossrefCites":0,"totalDimensionsCites":0,"hasAltmetrics":0,"orderNumber":2,"abstract":"\u003Cp id=\"p1\"\u003EHydrocephalus is a broad term usually understood as cerebrospinal fluid (CSF) accumulation resulting in cerebral ventricular system expansion. The production of CSF is by the choroid plexus in lateral ventricles, flowing between the third and fourth ventricles and eventually to the subarachnoid space. It is critical for proper neuronal function. Hydrocephalus is a neurological pathology linked to high morbidity from neurocognitive and motor impairment. It is classified as either communicating or non-communicating. Communicating hydrocephalus is understood as a deficit at cranial arachnoid villi and granulation absorption sites. However, there has been evidence that extracranial lymphatic vessels in the ethmoid bone region also play a role indicated by decreased lymphatic absorption in rat models of hydrocephalus. Treatment typically involves surgical shunt placement or endoscopic third ventriculostomy (ETV) technique with or without choroid plexus cauterization (CPC). These surgical interventions have high failure risks and complications that require re-intervention, further increasing morbidity and mortality risks. To date, there are few nonsurgical treatment strategies, but many have proved limited benefit, and many patients still require surgery. This analysis lays out the typical treatments and explores new, innovative interventions by highlighting the active role of brain parenchymal tissue in the pathogenesis of hydrocephalus.\u003C\u002Fp\u003E\n","signatures":"Sarah Arianna Mirkhaef, Lauren Harbaugh and Gurjit Nagra","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F1167866","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F1167866","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"557380","title":"Assistant Prof.","name":"Gurjit","surname":"Nagra","slug":"gurjit-nagra","fullName":"Gurjit Nagra"},{"id":"565312","title":"B.A.","name":"Sarah","surname":"Mirkhaef","slug":"sarah-mirkhaef","fullName":"Sarah Mirkhaef"},{"id":"565314","title":"M.Sc.","name":"Lauren","surname":"Harbaugh","slug":"lauren-harbaugh","fullName":"Lauren Harbaugh"}],"corrections":null,"_preview":0},{"id":"1168118","title":"Clinical Aspects in Which Symptoms May Indicate Cerebrospinal Fluid (CSF) Analysis","doi":"10.5772\u002Fintechopen.1003140","slug":null,"totalDownloads":36,"totalCrossrefCites":0,"totalDimensionsCites":0,"hasAltmetrics":0,"orderNumber":3,"abstract":"\u003Cp id=\"p1\"\u003EThis chapter aims to describe clinical aspects in which examination of cerebrospinal fluid is essential for diagnosis. Clinical signs and symptoms that may indicate analysis of cerebrospinal fluid may include changes in mental status, severe headache, difficulty speaking, difficulty walking, dizziness, fever, muscle weakness, sensitivity to light, and seizures. Cerebrospinal fluid is frequently collected by lumbar puncture—a procedure of mainly diagnostic value. Examination of the cerebrospinal fluid determines the appearance, chemical and cytological composition, and pressure. In some conditions, analysis of cerebrospinal fluid is no longer necessary to establish the diagnosis, but the presence of changes in cerebrospinal fluid increases the level of “comfort” for diagnosis. Today, the lumbar puncture is no longer used to examine all types of central nervous system disorders. However, it is still used to diagnose central nervous system infections, neuro-immunological disorders, tumours, Guillain-Barré syndrome, and multiple sclerosis.\u003C\u002Fp\u003E\n","signatures":"Mariana-Alis Neagoe","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F1168118","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F1168118","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"557646","title":"Assistant Prof.","name":"Mariana-Alis","surname":"Neagoe","slug":"mariana-alis-neagoe","fullName":"Mariana-Alis Neagoe"}],"corrections":null,"_preview":0},{"id":"1167648","title":"Basic CSF Tests Should Go beyond Early in Atypical Presentations of Brain Infections","doi":"10.5772\u002Fintechopen.1004228","slug":null,"totalDownloads":8,"totalCrossrefCites":0,"totalDimensionsCites":0,"hasAltmetrics":0,"orderNumber":4,"abstract":"\u003Cp id=\"p1\"\u003EThe spectrum of infections in the central nervous system (CNS) has dramatically changed over centuries, attributing to high rate of microbial replication, mutations, and expansion across the new geographical regions. Vaccination reduced the burden of bacterial meningitis; however, serotype replacement, for example, \u003Cem\u003E\u003Citalic xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES. pneumoniae\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E remains a problem. Urgent blood and cerebrospinal fluid (CSF) sampling is recommended unless lumbar puncture is contraindicated. CSF Gram stain and culture, serology, and polymerase chain reaction (PCR) are the basic tests in isolating the organism. About 40 to 60% of CNS infections has undetermined diagnosis due to lack of standardised diagnostic tests and clinical case definitions that may lead to inappropriate use of antibiotics or untreated infection with long-term sequelae. Among case examples, Lyme cerebellitis presents with ataxia and nystagmus, with diagnostic delay and resultant delay in treatment. Early inclusion of specific advanced tests on CSF, molecular diagnostics serology, and next-generation sequencing (NGS) involves a comprehensive quantitative analysis of all pathogens. CfDNA has high sensitivity (75–91%) and specificity (81–100%) to detect any intracellular or extracellular pathogens. Early inclusion of CSF basic tests to beyond by including current evidence-based technology tools in conjunction with clinical presentation could improve quality in diagnosing early, any rare brain infections.\u003C\u002Fp\u003E\n","signatures":"Kanwal Altaf Malik, Babu Paturi and Stephane Maingard","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F1167648","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F1167648","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"557159","title":"Dr.","name":"Babu","surname":"Paturi","slug":"babu-paturi","fullName":"Babu Paturi"},{"id":"561258","title":"Dr.","name":"Kanwal","surname":"Altaf Malik","slug":"kanwal-altaf-malik","fullName":"Kanwal Altaf Malik"},{"id":"561263","title":"Dr.","name":"Stephane","surname":"Maingard","slug":"stephane-maingard","fullName":"Stephane Maingard"}],"corrections":null,"_preview":0},{"id":"1175678","title":"Complementary Technologies for CSF Biomarker Analysis","doi":"10.5772\u002Fintechopen.1004355","slug":null,"totalDownloads":14,"totalCrossrefCites":0,"totalDimensionsCites":0,"hasAltmetrics":0,"orderNumber":5,"abstract":"\u003Cp id=\"p1\"\u003ECerebrospinal fluid (CSF) is a metabolically active body fluid that contains rich categories of circulating biomarkers, including cells (e.g., leukocytes, cancer cells), extracellular vesicles (e.g., apoptotic bodies, microvesicles and exosomes) and molecules (e.g., amyloid β aggregates, tau proteins, microRNAs and interleukins). These biomarkers have been studied in patients with various neurologic diseases such as seizure disorders, Alzheimer’s disease, glioblastoma, inflammation, traumatic brain injury, etc. Conventional CSF analysis uses flow cytometry, ELISA, mass spectroscopy qPCR, etc. for biomarker profiling. These approaches can provide comprehensive proteomics or transcriptomics analyses but require large sample volume, bulky and expensive equipment, and extensive processing and\u002For detection time. With emerging micro\u002Fnanotechnologies, new opportunities have been offered for rapid, accurate, and early diagnostics. These new technologies, including microfluidic system, magnetic biosensors (e.g., μNMR, μHall, GMR), optical biosensors (e.g., SPR), and electrochemical biosensors, can provide size-matching methodologies for biomarker isolation and detection in complex bio-fluids.\u003C\u002Fp\u003E\n","signatures":"Li Zhang","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F1175678","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F1175678","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"authors":[{"id":"571035","title":"Dr.","name":"Li","surname":"Zhang","slug":"li-zhang","fullName":"Li Zhang"}],"corrections":null,"_preview":0}]},"relatedBooks":[{"type":"book","id":"11893","title":"Cerebral Palsy","subtitle":"Updates","isOpenForSubmission":false,"isPublished":true,"hash":"5d00ebf9e29ea22b407add235839e4f8","slug":"cerebral-palsy-updates","bookSignature":"Pinar Kuru Bektaşoğlu","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F11893.jpg","editedByType":"Edited by","editors":[{"id":"244230","title":"Dr.","name":"Pinar","surname":"Kuru Bektasoglu","slug":"pinar-kuru-bektasoglu","fullName":"Pinar Kuru Bektasoglu"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null,"productType":{"id":"1","chapterContentType":"chapter","authoredCaption":"Edited by"}},{"type":"book","id":"6907","title":"Feed Your Mind","subtitle":"How Does Nutrition Modulate Brain Function throughout Life?","isOpenForSubmission":false,"isPublished":true,"hash":"91a663d09b6d6e80db3a69fca11e5b68","slug":"feed-your-mind-how-does-nutrition-modulate-brain-function-throughout-life-","bookSignature":"Clémentine Bosch-Bouju, Sophie Layé and Véronique Pallet","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F6907.jpg","editedByType":"Edited by","editors":[{"id":"265901","title":"Dr.","name":"Clémentine","surname":"Bosch-Bouju","slug":"clementine-bosch-bouju","fullName":"Clémentine Bosch-Bouju"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null,"productType":{"id":"1","chapterContentType":"chapter","authoredCaption":"Edited by"}},{"type":"book","id":"6991","title":"Neurons","subtitle":"Dendrites and Axons","isOpenForSubmission":false,"isPublished":true,"hash":"696489f55e1077935f47087fa3829b5f","slug":"neurons-dendrites-and-axons","bookSignature":"Gonzalo Emiliano Aranda Abreu and María Elena Hernández Aguilar","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F6991.jpg","editedByType":"Edited by","editors":[{"id":"72314","title":"Dr.","name":"Gonzalo Emiliano","surname":"Aranda Abreu","slug":"gonzalo-emiliano-aranda-abreu","fullName":"Gonzalo Emiliano Aranda Abreu"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null,"productType":{"id":"1","chapterContentType":"chapter","authoredCaption":"Edited by"}},{"type":"book","id":"6808","title":"Autonomic Nervous System","subtitle":null,"isOpenForSubmission":false,"isPublished":true,"hash":"d95e7c43f124d1a6e39b88862a917fc1","slug":"autonomic-nervous-system","bookSignature":"Pavol Svorc","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F6808.jpg","editedByType":"Edited by","editors":[{"id":"169212","title":"Prof.","name":"Pavol","surname":"Švorc","slug":"pavol-svorc","fullName":"Pavol Švorc"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null,"productType":{"id":"1","chapterContentType":"chapter","authoredCaption":"Edited by"}},{"type":"book","id":"6899","title":"Chronobiology","subtitle":"The Science of Biological Time Structure","isOpenForSubmission":false,"isPublished":true,"hash":"521dfb38a216470da6f8f7d02469832c","slug":"chronobiology-the-science-of-biological-time-structure","bookSignature":"Pavol Svorc","coverURL":"https:\u002F\u002Fcdn.intechopen.com\u002Fbooks\u002Fimages_new\u002F6899.jpg","editedByType":"Edited by","editors":[{"id":"169212","title":"Prof.","name":"Pavol","surname":"Švorc","slug":"pavol-svorc","fullName":"Pavol Švorc"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null,"productType":{"id":"1","chapterContentType":"chapter","authoredCaption":"Edited by"}},{"type":"book","id":"6786","title":"Optic Nerve","subtitle":null,"isOpenForSubmission":false,"isPublished":true,"hash":"b21864e6a0b3b316480d18efda1e18ee","slug":"optic-nerve","bookSignature":"Felicia M. 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This book will be designed for researchers, engineers, and even students in relevant research fields. An Introduction to condensation and boiling will be the first step in this book, which will be followed by a detailed explanation of the mechanisms for both condensation and boiling. Many topics will be covered, including two-phase flow modeling, nucleation theory, and cutting-edge industrial applications, such as the enhancement of heat transfer, micro- and macro-channels, numerical strategies and experimental techniques (visualization for bubble formation and development), and so on. With a strong emphasis on both theoretical understanding and practical insights, this book can bridge the gap between classic heat transfer concepts and the latest advancements, applying it to renewable energy systems, heat recovery systems, and carbon neutrality. Unresolved challenges will also be pointed out at the end of this book.","isbn":"978-1-83635-216-7","printIsbn":"978-1-83635-217-4","pdfIsbn":"978-1-83635-218-1","doi":"10.5772\u002Fintechopen.1006435","price":0,"priceEur":null,"priceUsd":null,"oapfPrice":1400,"slug":null,"numberOfPages":0,"isOpenForSubmission":true,"isSalesforceBook":true,"isNomenclature":false,"hash":"506bb40ae2e390e5b81796b153b40551","bookSignature":"Dr. Peixin Dong","publishedDate":null,"coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc0000091cJnIAI\u002F0016410_TrikoderCover%20%282024-07-30%2009%3A09%3A26%29.jpg","cdnCoverURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1004506\u002F1731500771-943002280\u002Fcover.jpg","cdnCoverURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1004506\u002F1731500771-943002280\u002Fcover-300.jpg","cdnWebCoverURL":null,"cdnWebCoverURL300":null,"cdnCoverWithTextURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1004506\u002F1731660716-610376127\u002Fcover-text.jpg","cdnCoverWithTextURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1004506\u002F1731660716-610376127\u002Fcover-text-300.jpg","keywords":"Two-Phase Flow, Flow Instability, Flow Regime, Heat Exchange, CFD Modelling, Heat Exchanger Design, Thermal Performances, Refrigeration, Heat Pipe, Superhydrophobic Surfaces, Superhydrophilic Surfaces, Cryogenic System","numberOfDownloads":null,"numberOfWosCitations":null,"numberOfCrossrefCitations":0,"numberOfDimensionsCitations":0,"numberOfTotalCitations":0,"isAvailableForWebshopOrdering":true,"dateEndFirstStepPublish":"November 20th 2024","dateEndSecondStepPublish":"December 23rd 2024","dateEndThirdStepPublish":"February 19th 2025","dateEndFourthStepPublish":"May 10th 2025","dateEndFifthStepPublish":"July 9th 2025","dateConfirmationOfParticipation":"December 18th 2024","remainingDaysToSecondStep":"a month","secondStepPassed":false,"areRegistrationsClosed":false,"currentStepOfPublishingProcess":2,"editedByType":null,"kuFlag":false,"sdgRelated":false,"biosketch":"An early career researcher in heat transfer, Hong Kong ITF postdoc, and holder of two registered patents.","equalEditorOneBiosketch":null,"equalEditorTwoBiosketch":null,"equalEditorThreeBiosketch":null,"coeditorOneBiosketch":null,"coeditorTwoBiosketch":null,"coeditorThreeBiosketch":null,"coeditorFourBiosketch":null,"coeditorFiveBiosketch":null,"isPublished":false,"isDeactivated":false,"editors":[{"id":"564212","title":"Dr.","name":"Peixin","middleName":null,"surname":"Dong","slug":"peixin-dong","fullName":"Peixin Dong","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F564212\u002F1727696805\u002Fprofile\u002Fimage1.jpg","biography":"Peixin Dong obtained his Ph.D. from the University of Queensland, Australia, and is a researcher at The Hong Kong University of Science and Technology, working on leakage or blockage detection based on time reversal. Before that, he finished two-years postdoctoral training. He has published more than thirty academic journal papers on heat transfer, twelve as first author and corresponding author. His research interests include natural draft dry cooling towers, printed circuit heat exchangers, electric vertical take-off and landing (eVTOL), aircraft thermal management, and wave propagations. He has been selected for the Hong Kong ITF-Talent Hub 2024. His mission and dedication are investigating the best solution for the thermal management of eVTOLs, which are expected to relieve urban congestion.","institutionString":null,"countryString":null,"position":null,"outsideEditionCount":null,"totalCites":0,"totalAuthoredChapters":"1","totalChapterViews":"0","totalEditedBooks":"1","institution":{"name":"Hong Kong University of Science and Technology","institutionURL":null,"country":{"name":"China"}}}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null,"coeditorOne":null,"coeditorTwo":null,"coeditorThree":null,"coeditorFour":null,"coeditorFive":null,"assistantEditorOne":null,"assistantEditorTwo":null,"assistantEditorThree":null,"assistantEditorFour":null,"assistantEditorFive":null,"topics":[{"id":"121","title":"Mechanical Engineering","slug":"mechanical-engineering"}],"chapters":null,"productType":{"id":"1","title":"Edited Volume","chapterContentType":"chapter","authoredCaption":"Edited by"},"subseries":null,"personalPublishingAssistant":{"id":"301331","firstName":"Mia","lastName":"Vulovic","middleName":null,"title":"Mrs.","imageUrl":"https:\u002F\u002Fmts.intechopen.com\u002Fstorage\u002Fusers\u002F301331\u002Fimages\u002F8498_n.jpg","email":"mia.v@intechopen.com","biography":"As an Author Service Manager, my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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The material properties, needed in design, can only sometimes be found in data sheets. If they are not available, they must be obtained by testing, for example the strength of a new alloy or concrete or the fatigue resistance of a vehicle part. Also, the manufacturers of electrical components must provide the reliability data for catalogs (e.g. the failure rate and the data characterizing the influence of some factors, such as temperature or vibrations). It is also impossible to predict with 100% accuracy the properties of a new bridge, an engine or a complex system consisting of many parts, whose properties vary more or less around the nominal values. In all these cases, tests are often necessary to verify whether the object has the demanded properties or if it conforms to the standards. Also, the information on loads (e.g. wind velocities in an unknown area) must often be obtained by measurement.\u003C\u002Fp\u003E\u003Cp id=\"P3\"\u003EThe reliability tests can be divided into two groups: those for providing detailed information on properties of new materials or components, and those for the verification of the expected values. The former are more extensive, as they must provide the mean value and statistical parameters characterizing the random variability. The extent of verification tests is smaller.\u003C\u002Fp\u003E\u003Cp id=\"P4\"\u003EIn this chapter, the reliability tests of mass-produced components will be described first, followed by the tests of large or complex structures or components and the tests of strength and fatigue resistance.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_2\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E1. Testing of mass-produced electrical and mechanical components\u003C\u002Fh2\u003E\u003Cp id=\"P5\"\u003EThe most important reliability characteristics are the mean failure rate and the mean time to failure or between failures. The tests can be done so that several components are loaded in a usual way (e.g. by electric current), and the times to failure of individual pieces are measured. As the time to failure of some samples can be very long, the test is sometimes terminated after failure of several pieces, at time \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E. The total cumulated time of operation to failure is calculated generally as\u003C\u002Fp\u003E\u003Cdiv id=\"df_E1\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext\u003Etot\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mo\u003E∑\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ej\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Em\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mi\u003Ej\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E...\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn001.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE1\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P6\"\u003Ewhere \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef,j\u003C\u002Fsub\u003E is the time to failure of \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ej\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E-th piece, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the number of failed specimens, and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Em\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the number of pieces that have survived the test, whose duration was \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E. The total number of all checked samples is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E + \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Em\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E. If all pieces have failed during the test, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Em\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 0 and the term \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Emt\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E falls out. (Also other test arrangements are possible, for example with replacing the failed pieces by good ones; see [\u003Ca href=\"#B1\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E1\u003C\u002Fa\u003E] or the corresponding IEC standards listed in Appendix 2. The mean time to failure is calculated as\u003C\u002Fp\u003E\u003Cdiv id=\"df_E2\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003EM\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext\u003Etot\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn002.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE2\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P7\"\u003EThe individual times to failure vary, and this must also be characterized. If failures occur due to various reasons, an exponential distribution of times to failure is often assumed. A simple check of this is the standard deviation \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eσ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E. For exponential distribution, the standard deviation has the same value as the mean \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eμ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E (in an ideal case; in real tests it can somewhat differ). If the difference between \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eμ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eσ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is larger, a statistical test should be made to check whether the exponential distribution is suitable. Common for this purpose are the goodness-of-fit tests (e.g. Kolmogorov-Smirnov or the \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E test); see [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E - \u003Ca href=\"#B4\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E4\u003C\u002Fa\u003E]. If exponential distribution is not suitable, another distribution can be better, e.g. Weibull.\u003C\u002Fp\u003E\u003Cp id=\"P8\"\u003EIf an exponential distribution is acceptable, the estimate of the mean failure rate can be obtained easily as the reciprocal value of the mean time to failure,\u003C\u002Fp\u003E\u003Cdiv id=\"df_E3\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E¯\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EM\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E.\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn003.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE3\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P9\"\u003EThe two-sided confidence interval for the true mean failure rate \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is [\u003Ca href=\"#B1\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E1\u003C\u002Fa\u003E]:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E4\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo stretchy=\"false\"\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo stretchy=\"false\"\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E¯\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo stretchy=\"false\"\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo stretchy=\"false\"\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E¯\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EU\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E.\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn004.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE4\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P10\"\u003Eif the testing was terminated at the \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003Eth failure, and\u003C\u002Fp\u003E\u003Cdiv id=\"df_E5\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E¯\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo stretchy=\"false\"\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo stretchy=\"false\"\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E&emsp;\u003C\u002Fmml:mtext\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EU\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E¯\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo stretchy=\"false\"\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mo stretchy=\"false\"\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E&emsp;\u003C\u002Fmml:mtext\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn005.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE5\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P11\"\u003Eif the testing continued come time after the \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003Eth failure. In \u003Ca href=\"#E4\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEquations (4\u003C\u002Fa\u003E) and (\u003Ca href=\"#E5\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003E5\u003C\u002Fa\u003E), \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the calculated mean value of \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, the subscripts \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EL\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EU\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E denote the lower and upper confidence limit, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E\u003Csub\u003E1 –α\u002F2\u003C\u002Fsub\u003E(2\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E) is the (1-\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u002F2)-critical value of the chi-square distribution for 2\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E degrees of freedom, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E\u003Csub\u003Eα\u002F2\u003C\u002Fsub\u003E(2\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E) is the α\u002F2-critical value for 2\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E degrees of freedom, and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E\u003Csub\u003Eα\u002F2\u003C\u002Fsub\u003E(2\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E+2) is the α\u002F2-critical value for 2\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E+2 degrees of freedom. The probability that \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E will lie within this confidence interval is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eγ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 1 – \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E. Often, we are interested only in the maximum expectable failure rate; the pertinent formula for the upper limit of one-sided interval is\u003C\u002Fp\u003E\u003Cdiv id=\"df_E6\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EU\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo stretchy=\"false\"\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo stretchy=\"false\"\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn006.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE6\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P12\"\u003Ethe probability that the actual failure rate will be higher is now \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E. As the mean time to failure failure is the reciprocal of the failure rate, the corresponding two-sided confidence interval for the mean time to failure is obtained as\u003C\u002Fp\u003E\u003Cdiv id=\"df_E7\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EL\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo stretchy=\"false\"\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo stretchy=\"false\"\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mi\u003EM\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E¯\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E≤\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo stretchy=\"false\"\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mo stretchy=\"false\"\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mi\u003EM\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EF\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EU\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn007.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE7\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P13\"\u003Eif the test was terminated after the \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003Eth failure (and analogously for a longer test).\u003C\u002Fp\u003E\u003Cp id=\"P14\"\u003EThe determination and importance of confidence limits will be illustrated on the following examples.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_3\" data-lvl=\"1\"\u003E\u003Cp\u003E\u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EExample 1\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\u003Cp id=\"P15\"\u003ETen electrical components were tested to determine the failure rate. The tests were terminated after \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003ET\u003C\u002Fsub\u003E = 500 h. During this time, six components failed (\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 6), in times: 65, 75, 90, 120, and 410 h. Four components survived the test. Estimate the mean time to failure and failure rate and construct two-sided confidence intervals (for confidence \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 90%).\u003C\u002Fp\u003E\u003Cp id=\"P16\"\u003ESolution. The mean value and standard deviation of the times to failure of the six failed components were 168.66 and 136.33 h, respectively. It is thus possible to assume exponential distribution.\u003C\u002Fp\u003E\u003Cp id=\"P17\"\u003EThe cumulated duration of tests, calculated after [\u003Ca href=\"#B1\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E1\u003C\u002Fa\u003E], was:\u003C\u002Fp\u003E\u003Cdiv id=\"df_BB1\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Eo\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003Cmml:mstyle displaystyle=\"true\"\u003E\u003Cmml:msubsup\u003E\u003Cmml:mo\u003E∑\u003C\u002Fmml:mo\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ei\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mn\u003E6\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msubsup\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mstyle\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mi\u003Ei\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E60\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E75\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E90\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E120\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E250\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E410\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E+\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E4\u003C\u002Fmml:mn\u003E\u003Cmml:mo\u003E×\u003C\u002Fmml:mo\u003E\u003Cmml:mn\u003E500\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mn\u003E3010\u003C\u002Fmml:mn\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mi\u003Eh\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E.\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn008.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EBB1\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P18\"\u003EThe mean time to failure is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E = \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Etot\u003C\u002Fsub\u003E\u002F\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 3010\u002F6 = 501.67 h, and the mean failure rate is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E = \u003Cspan class=\"inline-formula\"\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\"\u003E\u003Cmml:mover accent=\"true\"\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mo\u003E¯\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mover\u003E\u003C\u002Fmml:math\u003E\u003C\u002Fspan\u003E = 1\u002F\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E = 1\u002F501.67 = 1.993 × 10\u003Csup\u003E-3\u003C\u002Fsup\u003E h\u003Csup\u003E-1\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp id=\"P19\"\u003EThe lower and upper confidence limits for \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E were calculated, with respect that the tests were terminated before the failure of all samples, according to \u003Ca href=\"#E5\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEquation (5\u003C\u002Fa\u003E). With \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 6 and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 10%, the critical values are \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E\u003Csub\u003E 0.95\u003C\u002Fsub\u003E(12) = 5.226 and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E\u003Csub\u003E 0.5\u003C\u002Fsub\u003E(14) = 23.685. Inserting them, together with \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E = 1.993 × 10\u003Csup\u003E-3\u003C\u002Fsup\u003E h\u003Csup\u003E-1\u003C\u002Fsup\u003E into (5) gives \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EL\u003C\u002Fsub\u003E = 8.68 × 10\u003Csup\u003E– 4\u003C\u002Fsup\u003E h\u003Csup\u003E– 1\u003C\u002Fsup\u003E and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EU\u003C\u002Fsub\u003E = 3.93 × 10\u003Csup\u003E–3\u003C\u002Fsup\u003E h\u003Csup\u003E– 1\u003C\u002Fsup\u003E. The confidence limits for the mean time to failure are \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EL\u003C\u002Fsub\u003E = 1\u002F\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EU\u003C\u002Fsub\u003E = 254.4 h and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EU\u003C\u002Fsub\u003E = 1\u002F\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EL\u003C\u002Fsub\u003E = 1152.1 h. The mean time to failure thus can lie within the interval \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E ∈ (254 h; 1152 h).\u003C\u002Fp\u003E\u003Cp id=\"P20\"\u003EAs we can see from this example, the confidence interval obtained from only six failures is very wide. If it should be narrower (to get more accurate estimate), it is necessary either to make a longer test so that more parts of the tested group fail or to increase the number of parts tested simultaneously or both.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_4\" data-lvl=\"1\"\u003E\u003Cp\u003E\u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EExample 2\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\u003Cp id=\"P21\"\u003EThe above testing has continued until the time \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E = 1000 h. During this time, two more pieces failed, at the times \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E7\u003C\u002Fsub\u003E = 520 h and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E8\u003C\u002Fsub\u003E = 760 h.\u003C\u002Fp\u003E\u003Cp id=\"P22\"\u003ESolution. The same procedure as above has given the following results: \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EΤ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 4290 h and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 8, so that the mean time to failure is now \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E = \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E \u002F\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 4290\u002F8 = 536 h and the mean failure rate \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E = 1\u002F536 = 1.865 × 10\u003Csup\u003E– 3\u003C\u002Fsup\u003E h\u003Csup\u003E– 1\u003C\u002Fsup\u003E. Also, the confidence interval will respect that more pieces have failed. The critical values now are \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E\u003Csub\u003E 0.95\u003C\u002Fsub\u003E(16) = 7.962 and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eχ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csup\u003E2\u003C\u002Fsup\u003E\u003Csub\u003E 0.5\u003C\u002Fsub\u003E(18) = 28.869. With all these values, the lower and upper limits of failure rate are \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EL\u003C\u002Fsub\u003E = 9.28×10\u003Csup\u003E– 4\u003C\u002Fsup\u003E h\u003Csup\u003E– 1\u003C\u002Fsup\u003E and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003EU\u003C\u002Fsub\u003E = 3.4×10\u003Csup\u003E– 3\u003C\u002Fsup\u003E h\u003Csup\u003E– 1\u003C\u002Fsup\u003E. The mean time to failure \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Emean\u003C\u002Fsub\u003E thus can be expected to lie within the interval (297 h; 1078 h).\u003C\u002Fp\u003E\u003Cp id=\"P23\"\u003EThe whole test lasted twice as long as the previous one, but the new confidence interval is only slightly narrower. If significantly more accurate estimates should be achieved, much longer tests or with substantially higher number of tested pieces must be done. Thus, when preparing the tests for the determination of failure rate, one should estimate in advance the duration of the test, the number of tested pieces, and the number of pieces that can fail — all this for the acceptable probability \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E that the actual maximum failure rate would be higher than that obtained from the test.\u003C\u002Fp\u003E\u003Cp id=\"P24\"\u003EThe rearrangement of the expression for the upper limit of confidence interval for \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E gives the following relationship between the expected failure rate \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E, the number of tested samples \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, test duration \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E, and the number of failed components \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E [\u003Ca href=\"#B1\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E1\u003C\u002Fa\u003E]:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E8\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003En\u003C\u002Fmml:mi\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003Eχ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:msub\u003E\u003Cmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mi\u003Eα\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mrow\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E0\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E.\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn010.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE8\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P25\"\u003EIf the number of failed samples does not exceed \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Er\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, the actual failure rate is not higher than \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E0\u003C\u002Fsub\u003E, the risk of wrong prediction being \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E.\u003C\u002Fp\u003E\u003Cp id=\"P26\"\u003EAs it follows from the product \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E × \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E in \u003Ca href=\"#E8\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEquation (8\u003C\u002Fa\u003E), the number of tested parts \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is equivalent to the test duration \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E. This means that the same information can be obtained by testing, for example, 10 specimens for 1000 h or 1000 specimens for 10 h. If the tested objects are expensive, one would prefer testing fewer specimens for longer time. However, at least several pieces should always be tested to reduce the risk that the only piece chosen at random for the test was especially good or especially bad.\u003C\u002Fp\u003E\u003Cp id=\"P27\"\u003EThe following table, based on \u003Ca href=\"#E8\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEquation (8\u003C\u002Fa\u003E), shows the values of the product \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E × \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E for the various numbers of failed parts during the tests; the probability of a wrong result is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 10%.\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" id=\"T1\"\u003E\u003Cdiv class=\"table-content\"\u003E\u003Ctable margin-left=\"0\"\u003E\n\t\t\u003Ccol width=\"122.85\"\u003E\n\t\t\u003Ccol width=\"122.85\"\u003E\n\t\t\u003Ccol width=\"122.85\"\u003E\n\t\t\u003Cthead\u003E\u003Ctr\u003E\n\t\t\t\u003Ctd border-top=\"1\" border-bottom=\"1\" border-left=\"0\" border-right=\"0\"\u003E\n\t\t\t\t\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003Csub\u003E0\u003C\u002Fsub\u003E(h\u003Csup\u003E-1\u003C\u002Fsup\u003E)\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\n\t\t\t\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\"1\" border-bottom=\"1\" border-left=\"0\" border-right=\"0\"\u003E\n\t\t\t\t\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En × t for r = 3\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\n\t\t\t\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\"1\" border-bottom=\"1\" border-left=\"0\" border-right=\"0\"\u003E\n\t\t\t\t\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En × t for r = 5\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\n\t\t\t\u003C\u002Ftd\u003E\n\t\t\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\n\t\t\u003Ctr\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E0.001\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E5322\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E7994\u003C\u002Ftd\u003E\n\t\t\u003C\u002Ftr\u003E\n\t\t\u003Ctr\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E0.0001\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E53,223\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E79,936\u003C\u002Ftd\u003E\n\t\t\u003C\u002Ftr\u003E\n\t\t\u003Ctr\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E0.00001\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E532,232\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\".5\" border-left=\"0\" border-right=\"0\"\u003E799,359\u003C\u002Ftd\u003E\n\t\t\u003C\u002Ftr\u003E\n\t\t\u003Ctr\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\"1\" border-left=\"0\" border-right=\"0\"\u003E0.000001\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\"1\" border-left=\"0\" border-right=\"0\"\u003E5,322,320\u003C\u002Ftd\u003E\n\t\t\t\u003Ctd border-top=\".5\" border-bottom=\"1\" border-left=\"0\" border-right=\"0\"\u003E7,993,590\u003C\u002Ftd\u003E\n\t\t\u003C\u002Ftr\u003E\n\t\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-caption\"\u003E\u003Ch3 class=\"heading\"\u003ETable 1.\u003C\u002Fh3\u003E\u003Cdiv class=\"text\"\u003E\u003Cp id=\"P28\"\u003EExtent of tests for various failure rate and the number of failed pieces.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"text\"\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P30\"\u003EFor example, the reliability testing of components with assumed exponential distribution, failure rate \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 10\u003Csup\u003E-4\u003C\u002Fsup\u003E h\u003Csup\u003E-1\u003C\u002Fsup\u003E and the test terminated after the fifth failure, needs \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E × \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E = 79,936 ≈ 80,000 pieces × hour. Thus, for example, 100 components should be tested 800 h or 800 components for 100 h. If the expected failure rate were \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eλ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 10\u003Csup\u003E-6\u003C\u002Fsup\u003E h\u003Csup\u003E-1\u003C\u002Fsup\u003E, then \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E × \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Et\u003C\u002Fsub\u003E ≈ 8,000,000 pieces × hour, so that 10,000 components must be tested for 800 h or 100 components for 80,000 h. One can see that testing for proving the reliability of very reliable components becomes very difficult or impracticable. Therefore, various \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eaccelerated tests\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E are often used. One way, suitable for the items working periodically with pauses between the operations, such as switches or valves, eliminates the idle times: the switch is permanently switched on and off.\u003C\u002Fp\u003E\u003Cp id=\"P31\"\u003EAnother way to obtain the demanded reliability information sooner uses a higher intensity of load (e.g. higher mechanical load, higher electric stress or electric current, or more severe environment (e.g. higher temperature or vibrations). If this approach should be effective, one must know the mechanism of degradation and the relationship between the load intensity and the rate of degradation. For example, the rate of chemical processes, which are the cause of some failures, often depends on the temperature according to the Arrhenius equation:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E9\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Er\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mi\u003Eexp\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mi mathvariant=\"normal\"\u003EΔ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EE\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn011.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE9\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P32\"\u003E\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is a constant, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003E∆E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the activation energy, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ek\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the Boltzmann constant, and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is the absolute temperature (K). If the times to failure have exponential distribution, the failure rates or times to failure are related with the absolute temperatures as follows [\u003Ca href=\"#B1\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E1\u003C\u002Fa\u003E]:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E10\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Eλ\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E[\u003C\u002Fmml:mo\u003E\u003Cmml:mrow\u003E\u003Cmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mi mathvariant=\"normal\"\u003EΔ\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003EE\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mi\u003Ek\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mrow\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mo\u003E−\u003C\u002Fmml:mo\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:mfrac\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003ET\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mfrac\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E]\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn012.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE10\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P33\"\u003E\u003Ca href=\"#E10\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEquation (10\u003C\u002Fa\u003E) can be used for the determination of necessary temperature change from \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E to \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ET\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E if the test duration should be reduced from \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E to \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Et\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E.\u003C\u002Fp\u003E\u003Cp id=\"P34\"\u003ESimilarly, the number of cycles to fatigue failure of periodically loaded components can be reduced by increasing the characteristic stress or load amplitude \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EP\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E. The basic relationship, based on the Wöhler-like curve [\u003Ca href=\"#E1\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEquation (1\u003C\u002Fa\u003E) in Chapter 6], is\u003C\u002Fp\u003E\u003Cdiv id=\"df_E11\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003Et\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EC\u003C\u002Fmml:mi\u003E\u003Cmml:msup\u003E\u003Cmml:mrow\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E(\u003C\u002Fmml:mo\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E1\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E\u002F\u003C\u002Fmml:mo\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EP\u003C\u002Fmml:mi\u003E\u003Cmml:mn\u003E2\u003C\u002Fmml:mn\u003E\u003C\u002Fmml:msub\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mo\u003E)\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:mrow\u003E\u003Cmml:mi\u003En\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003E;\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn013.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE11\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P35\"\u003E\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EC\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E are constants for a given material and environment. Similar relationships can be used for finding the increased load for shortened tests of components exposed to creep or static fatigue (stress enhanced corrosion), with rates depending on some power of the load.\u003C\u002Fp\u003E\u003Cp id=\"P36\"\u003EToday, mass-produced electronic and electrical components are tested in special chambers and under special conditions enabling acceptably short duration of the tests. More about these tests, denoted \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EHALT\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E (for highly accelerated life testing) or \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EHASS\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E (for highly accelerated stress screening), can be found in the literature, for example [\u003Ca href=\"#B5\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E5\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"P37\"\u003E\u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ESorting tests\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\u003Cp id=\"P38\"\u003EThese tests aim at sorting out “weak” items that could fail shortly after being put into service. However, they must not cause excessive degradation of properties in “good” components (i.e. they should not shorten their life significantly). Sorting tests can be nondestructive or destructive. \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ENondestructive tests\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E use visual observation, X-ray, ultrasound or magnetic inspection, and special electrical or other measurements. \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EDestructive tests\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E can be arranged in several ways, for example \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eproof tests\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E that use short-time overloading by mechanical or electrical stress exceeding the nominal value so that the weak parts are destroyed during the test. Other ways for revealing the weak parts are artificial aging under increased temperature, cyclic loading by varying temperatures (this causes additional thermal stresses that can reveal hidden defects or weak joints), the use of burn-in period with 75% to 100% of nominal load acting several tens of hours before putting into service, special kinds of mechanical loading, such as impacts, vibrations of certain amplitude, and frequency, overloading of rotating parts by centrifugal forces and others.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_5\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E2. Acceptance sampling\u003C\u002Fh2\u003E\u003Cp id=\"P39\"\u003EThis operation, common in series production, ensures that only those batches of items will be released to the customer or to the next operation, which are either perfect or contain only very small proportion of out-of-tolerance parts. Before this control is introduced, a test plan must be prepared, which contains:\u003C\u002Fp\u003E\u003Col style=\"list-style-type: order;\"\u003E\u003Cli\u003E\u003Cp id=\"P40\"\u003EKinds of monitored indicators,\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"P41\"\u003ENumber of tested items,\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"P42\"\u003EDuration of the tests,\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"P43\"\u003ECriterion for the decision on the acceptance.\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003Cp id=\"P44\"\u003EGenerally, three approaches are used:\u003C\u002Fp\u003E\u003Col style=\"list-style-type: alpha-lower;\"\u003E\u003Cli\u003E\u003Cp id=\"P45\"\u003E\u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003E100% control.\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E Every component or item must pass the inspection, and those that do not fulfill certain parameters are discarded. This control is most expensive, but it should be the safest. Nevertheless, if the evaluation depends on human senses (visual check, for example) here, a small probability of erroneous decisions also exists. The inspector can overlook a defect or, vice versa, he can denote a good item as defective, especially if the number of tested items is very high, which can lead to his fatigue. An example is the check for internal flaws using X-rays, with the images interpreted via observation by naked eye. Also, 100% control cannot be done if every test ends with the destruction of the tested piece, even if it is good (e.g. the check of the airbag deployment system in cars).\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"P46\"\u003E\u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ERandom inspection.\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E Only several pieces, chosen at random, are tested (e.g. 1% of the batch). The entire lot is accepted or rejected according to the result of the inspection. This kind of acceptance is much less demanding than 100% control, but it has been criticized that it is rather subjective and not sufficiently reliable. If, for example, a batch of 10,000 pieces contains 1% of defective piece and it was decided that 1% will be tested, then 100 pieces must be checked. One percent of 100 is one piece. However, it can happen that the checked sample will contain not exactly one defective piece, but two or three or even none. This uncertainty has led to the development of the following method based on the probability theory.\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003Cli\u003E\u003Cp id=\"P47\"\u003E\u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EStatistical acceptance.\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E Several variants exist. The principle will be explained on the so-called \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Esingle sampling plan\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E. A sample of \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E pieces is taken at random from the lot and tested. The number \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E of out-of-tolerance pieces, found in the sample, is compared with the so-called \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Edecisive number\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E. If it is lower, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez < c\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, the whole lot is accepted; if \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez > c\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, it is rejected. The values of \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E for various expected proportions \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E of unsuitable pieces and extent \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E of the tested sample can be found in the standards for statistical acceptance [\u003Ca href=\"#B6\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E6\u003C\u002Fa\u003E] or calculated, with a consideration of further important parameters, \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EAQL\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E (acceptable quality level) and \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ELQL\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E (limiting quality level, also called the lot tolerance percent defective, \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ELTPD\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E). LQL gives the maximum fraction of defectives, acceptable, on average, in the batches denoted as good. The principle of determination of the decisive number \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is as follows. If the fraction of defectives in the population is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, the number \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E of the defectives that can appear in a random sample of size \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003En\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E has binomial or Poisson’s distribution (for low probabilities \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E in the latter case). It is thus possible to calculate the cumulative probabilities for \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E = 0, 1, 2, 3,... The decisive number \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is such that only very low probability \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eβ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E exists that the lot, whose test has given \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E ≤ \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, will contain higher percentage of defective than LQL. The probability \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003E\u003Cbold\u003Eβ\u003C\u002Fbold\u003E\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E is called \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ecustomer’s risk\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E and means the risk that an unsatisfactory lot will be accepted as good. On the other hand, also a \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eproducer’s risk \u003Citalic\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E exists, such that a good lot, with less defective pieces than AQL, will be rejected. Usually, 5% or 1% is chosen for both \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eβ\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E.\u003C\u002Fp\u003E\u003C\u002Fli\u003E\u003C\u002Fol\u003E\u003Cp id=\"P48\"\u003EThe curve showing how the probability of accepting the lot decreases with increasing proportion of defectives in the sample is called the \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eoperating characteristic curve\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E (OCC). \u003Ca href=\"#F1\" class=\"ref-link\" data-ref-style=\"fig\"\u003EFigure 1\u003C\u002Fa\u003E shows examples of OCCs for two different decisive numbers.\u003C\u002Fp\u003E\u003Cp id=\"preF1\"\u003EThe rejected batch is either discarded or 100% checked. In the latter case, the good pieces are added to other good items. This makes the average quality of the batches composed in this way better, so that the quality demands in the tests may slightly be reduced.\u003C\u002Fp\u003E\u003Cfigure class=\"media-panel\" id=\"F1\"\u003E\u003Cdiv class=\"media\"\u003E\u003Cimg src=\"\u002F\u002Fcdnintech.com\u002Fmedia\u002Fchapter\u002F50124\u002F1512345123\u002Fmedia\u002Fimage14_w.jpg\" class=\"figure-link\" alt=\"\"\u003E\u003C\u002Fdiv\u003E\u003Cfigcaption class=\"caption\"\u003E\u003Ch4\u003EFigure 1.\u003C\u002Fh4\u003E\u003Cp\u003E\u003Cp xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\" id=\"P50\"\u003EOperating characteristic curve (OCC). \u003Citalic\u003EP -\u003C\u002Fitalic\u003E probability of acceptance; \u003Citalic\u003Ep -\u003C\u002Fitalic\u003E percentage of defectives in the population; \u003Citalic\u003Eα –\u003C\u002Fitalic\u003E producer’s risk; \u003Citalic\u003Eβ –\u003C\u002Fitalic\u003E customer’s risk. Subscripts 1 and 2 denote curves OCC1 and OCC2.\u003C\u002Fp\u003E\u003C\u002Fp\u003E\u003C\u002Ffigcaption\u003E\u003C\u002Ffigure\u003E\u003Cp id=\"posleF1\"\u003EAlso other schemes exist. For example, a \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Edouble sampling scheme\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E uses two decisive numbers, \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E and \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E. If the number \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E of defectives in the first sample is smaller than \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E, the lot is accepted, and if it is higher than \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E, it is rejected. If \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E < \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ez\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E ≤ \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ec\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E, another sample is taken and the total number of defective in both samples is checked, etc. Further modifications, such as multiple sampling or sequential sampling, exist as well. For more, see [\u003Ca href=\"#B6\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E6\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"P52\"\u003EHowever, doubts are sometimes cast on the cost-effectivity of statistical control. On the one hand, this control costs money. On the other hand, losses can arise due to possible defective pieces hidden in the batches checked as good. Deming [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E] has pointed out that if the cost for inspection of one piece is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ek\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E and the average cost of a failure caused by not inspecting is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ek\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E and the average fraction of defective is \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, then, if \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Epk\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E < \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ek\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E, the lowest total costs (control costs plus costs caused by failures) will be achieved without any testing. If \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Epk\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E > \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ek\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E, full (100%) inspection should be used, especially for higher ratios \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Epk\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E2\u003C\u002Fsub\u003E\u002F\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ek\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003E1\u003C\u002Fsub\u003E. However, the situation is often not so simple; the fraction \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Ep\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E of defectives can vary, 100% testing can be impracticable for too high investment costs or if all tests end with destruction, etc.\u003C\u002Fp\u003E\u003Cp id=\"P53\"\u003EThe statistical acceptance was very popular in the second half of the 20th century but not so much today. There are two reasons: the demands on quality and reliability are much higher today than 50 years ago and the allowable probabilities are often of the order 1:10\u003Csup\u003E6\u003C\u002Fsup\u003E, much lower than the degree of confidence common in statistical sampling. Moreover, the controlling devices are much more powerful today. The incorporation of automated test equipment (\u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EATE\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E) into production line enables 100% control.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_6\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E3. Testing of large structures and complex components\u003C\u002Fh2\u003E\u003Cp id=\"P54\"\u003EThese tests will be illustrated on two cases: bridges and large components exposed to fatigue, such as parts of heavy vehicles (e.g. locomotives).\u003C\u002Fp\u003E\u003Cp id=\"P55\"\u003EThe assumed service life of road and railway bridges is many tens of years and sometimes more. During this time, the structure deteriorates and its safety decreases. Also, the loading pattern can change in a long time (new kinds of vehicles and changed traffic demands). For these reasons, bridges must sometimes be repaired or reconstructed. In such case, thorough inspections are done at suitable time, including \u003Cstrong\u003E\u003Cbold xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eload tests\u003C\u002Fbold\u003E\u003C\u002Fstrong\u003E in important cases. In these tests, the bridge is usually loaded by a group of trucks loaded by sand or concrete blocks as much as possible so that the load-carrying capacity of the bridge is attained. During the tests, deformations and stresses at selected points are measured and compared with the values obtained by computer analysis of the structure – to see if the actual response (e.g. deflection of some parts of the bridge) corresponds to the assumed response. In some cases, dynamic properties are also studied (i.e. the response to periodic or dynamic loading). If the actual condition is worse than allowed, measures must be taken for improvement.\u003C\u002Fp\u003E\u003Cp id=\"P56\"\u003ELarge parts of mechanical structures, such as vehicles or aircrafts (sometimes these objects as a whole), are mechanically loaded with the purpose to find whether the actual response (deformations and stresses at selected points) corresponds to the values assumed in design. Also, dynamic response is investigated. Exceptionally, the object is loaded until the destruction. In the past, the measurements were often the only reliable source of information of the stresses and behavior. Today, the methods of stress analysis are much better and much information can be obtained by computer simulation as early as in the design stage. Therefore, today the tests serve rather for confirmation whether the demanded parameters have been achieved.\u003C\u002Fp\u003E\u003Cp id=\"P57\"\u003EThe test loads are often imposed by electrohydraulic cylinders attached to the tested object. Often, special test stands are used, consisting of a massive frame with hydraulic cylinders, clamping equipment, and a controlling unit. The work of the stand is controlled by a computer. This enables one to program the demanded loading sequences. Sometimes, the load program is based on a record made during a test vehicle driving on real roads or on a test track containing typical examples of road surfaces. The test vehicle is equipped with sensors (usually strain gauges fixed at certain points of the car body) and the measured data are recorded. These data must be transformed to the data for the control of the load cylinders of the testing stand. The reason is that these cylinders are often attached to the tested structure at different points than were those used in the test vehicle driven on the track. Also, the data recorded with one test vehicle are sometimes used for the testing of other types of vehicles. The test stand can repeat the recorded load sequence again and again, so that also fatigue resistance can be tested in this way.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_7\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E4. Tests of strength and fatigue resistance\u003C\u002Fh2\u003E\u003Cp id=\"P58\"\u003EThese tests are often arranged according to various standards. In this paragraph, we thus limit our attention to some probabilistic aspects of these tests.\u003C\u002Fp\u003E\u003Cp id=\"P59\"\u003EStrength tests. The individual values vary, so that the number of tests should be adjusted to the purpose of the measurement and to the scatter of individual values. If only approximate information on the average strength is needed, three tests may be sufficient; the standard deviation can serve for the estimation of confidence interval of the mean strength. However, especially for brittle materials with high scatter of individual values, the knowledge of the ”minimum“ strength is often demanded. This is determined as a lowprobability quantile. For this purpose, more tests must be done, often several tens or more. From these tests, the parameters of strength distribution are determined. Often, Weibull distribution, but also log-normal distribution, is assumed. The determination of parameters and quantiles of Weibull distribution was described in Chapters 11 and 18. The parameters of log-normal distribution are found in several steps. In the first step, logarithms are taken from the measured values, then the average and standard deviation are calculated from the transformed data, and finally they are transformed back to the original system of units. The question of which distribution is better can be solved by means of statistical tests of goodness of fit [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E – \u003Ca href=\"#B4\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E4\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"P60\"\u003EGenerally, many values are necessary to obtain reliable values of low-probability quantiles of strength. (Remember that 1% quantile corresponds to the minimum of 100 values.)\u003C\u002Fp\u003E\u003Cp id=\"P61\"\u003EFatigue tests. The main purpose of fatigue tests is the determination of fatigue limit (if it exists) and finding the relationship between the characteristic stress (\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E) and the time or number of cycles to failure (\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef\u003C\u002Fsub\u003E). As for the fatigue limit, everything from the above paragraph on strength tests remains valid. The \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E relationship is obtained by making the tests under various characteristic stress amplitudes and fitting the data by a suitable function, for example [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E, \u003Ca href=\"#B9\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E9\u003C\u002Fa\u003E]:\u003C\u002Fp\u003E\u003Cdiv id=\"df_E12\" class=\"formula panel\"\u003E\u003Calternatives\u003E\u003Cmml:math xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" specific-use=\"web-only\" display=\"block\"\u003E\u003Cmml:mrow\u003E\u003Cmml:msub\u003E\u003Cmml:mi\u003EN\u003C\u002Fmml:mi\u003E\u003Cmml:mi\u003Ef\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:msub\u003E\u003Cmml:mo\u003E=\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003EA\u003C\u002Fmml:mi\u003E\u003Cmml:mtext\u003E \u003C\u002Fmml:mtext\u003E\u003Cmml:msup\u003E\u003Cmml:mi\u003ES\u003C\u002Fmml:mi\u003E\u003Cmml:mrow\u003E\u003Cmml:mo\u003E–\u003C\u002Fmml:mo\u003E\u003Cmml:mi\u003Ew\u003C\u002Fmml:mi\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:msup\u003E\u003Cmml:mo\u003E,\u003C\u002Fmml:mo\u003E\u003C\u002Fmml:mrow\u003E\u003C\u002Fmml:math\u003E\u003Cgraphic xmlns:NS2=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" specific-use=\"print-only\" NS2:href=\"media\u002FEqn014.wmf\"\u003E\u003C\u002Fgraphic\u003E\u003C\u002Falternatives\u003E\u003Cspan class=\"equ\"\u003EE12\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp id=\"P62\"\u003Eor a similar expression. Now, two possibilities exist depending on the number of tests that were done or could be done with respect to the available money and time. If only several tests have been performed, all measured \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef\u003C\u002Fsub\u003E(\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E) values are fitted by the regression function (12). The consequences of the scatter of individual values are depicted in Figure 1 in Chapter 18. The regression function, obtained by the least-squares method, gives such \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef\u003C\u002Fsub\u003E values that probability 50% exists that the true number of cycles to failure under a chosen stress will be 50% lower (!) than the number obtained from the regression function. The ”safe“ \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef,α\u003C\u002Fsub\u003E values, for which acceptably low probability \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E would exist that the component or construction can fail earlier, may be found as boundary values of the pertinent confidence band for all \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E-\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E data; see Chapter 18.\u003C\u002Fp\u003E\u003Cp id=\"P63\"\u003EIf more values (e.g. tens) are available for each stress level, a more accurate procedure can be used. The data for individual stress levels are rank-ordered in ascending order. Each value corresponds to some quantile of time to failure for a given stress level. For example, the shortest time of 10 values obtained for the same stress corresponds approximately to 10% quantile of the time to failure. Now, only the \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003EN\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003Csub\u003Ef,\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E\u003C\u002Fsub\u003E(\u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003ES\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E) values, corresponding to the same quantile \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E, are fitted by regression function (12). The “safety” of the prediction of the time to failure with this function \u003Ca href=\"#E1\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003Eequals 1\u003C\u002Fa\u003E – \u003Cem\u003E\u003Citalic xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\" xmlns:mml=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" xmlns:xsi=\"http:\u002F\u002Fwww.w3.org\u002F2001\u002FXMLSchema-instance\"\u003Eα\u003C\u002Fitalic\u003E\u003C\u002Fem\u003E. It is also possible to fit all measured data by function of type (12) with additional parameters characterizing the probability that the actual number of cycles to failure will be lower than that calculated via modified \u003Ca href=\"#E12\" class=\"ref-link\" data-ref-style=\"disp-formula\"\u003EEquation (12\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\n","keywords":"Random quantity, uncertainty, normal distribution, Weibull distribution, tolerance limits, correlation, interference method, Monte Carlo method, bootstrap 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characteristic values of random quantities (quantiles of normal and Weibull distribution, tolerance limits, linearly correlated data, interference method, Monte Carlo method, bootstrap method).","reviewType":"peer-reviewed","bibtexUrl":"\u002Fchapter\u002Fbibtex\u002F50124","risUrl":"\u002Fchapter\u002Fris\u002F50124","isPublished":true,"isOnlineFirst":false,"isDeactivated":0,"noAds":0,"subseries":null,"book":{"id":"5317","type":"book","title":"Concise Reliability for Engineers","subtitle":null,"fullTitle":"Concise Reliability for Engineers","slug":"concise-reliability-for-engineers","publishedDate":"April 13th 2016","bookSignature":"Jaroslav 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Introduction\u003C\u002Fh2\u003E\u003Cp id=\"p2\"\u003EUranium, the heaviest naturally occurring element, stands at the intersection of immense potential and significant risk. With an atomic weight surpassing those of all other naturally occurring elements, uranium contains 92 protons and 92 electrons, including 6 valence electrons [\u003Ca href=\"#B1\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E1\u003C\u002Fa\u003E]. As an alpha particle emitter, uranium undergoes a complex decay process, with its decay chain beginning with Uranium-238 (U-238) culminating in stable Lead-206 (Pb-206) [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E]. Discovered in 1789 by the German chemist Martin Heinrich Klaproth in a pitchblende specimen and named after the planet “Uranus,” uranium initially gained attention for its ability to create vibrant pigments [\u003Ca href=\"#B3\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E3\u003C\u002Fa\u003E]. However, its radioactive properties later unveiled far deeper significance, leading to transformative events in history, science, and medicine.\u003C\u002Fp\u003E\u003Cp id=\"p3\"\u003EUranium’s evolution from a material used in decorative arts to cornerstone of scientific discovery exemplifies the complex interplay of beauty, power, and scientific importance [\u003Ca href=\"#B4\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E4\u003C\u002Fa\u003E]. It is most widely recognized today for its critical role in fueling nuclear reactors, providing a powerful source of energy that drives electricity generation around the world [\u003Ca href=\"#B4\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E4\u003C\u002Fa\u003E]. This potent energy offers an alternative to fossil fuels and contributing to the global push for cleaner energy.\u003C\u002Fp\u003E\u003Cp id=\"p4\"\u003EHowever, as the world transitions toward sustainable energy solutions, the global demand for uranium is expected to rise, driving a surge in mining activities [\u003Ca href=\"#B5\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E5\u003C\u002Fa\u003E]. This, coupled with other anthropogenic factors such as waste and the use of agricultural fertilizers, is contributing to higher uranium levels in the environment, thereby heightening environmental and health concerns [\u003Ca href=\"#B6\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E6\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p5\"\u003EThis duality presents a profound challenge: how to maximize the benefits of uranium while minimizing its dangers. As the global demand for energy and medical advancements continues to increase, so too does the need for uranium. This chapter explores the dual nature of uranium, tracing its historical significance, scientific contributions, and environmental implications of its use. By understanding both the opportunities and the risks associated with uranium, we can better navigate the path forward in managing this powerful yet perilous element.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_2\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E2. Uranium in nature and its evolution\u003C\u002Fh2\u003E\u003Cp id=\"p6\"\u003EUranium is a naturally occurring element that is ubiquitously found in soils, minerals, and water bodies across the earth [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E]. It ranks as the 49th most abundant element in Earth’s crust and is lithophile, radioactive, and one of the heaviest naturally occurring elements [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E]. Uranium is considered one of the primordial elements that were present in the Earth’s formation [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E]. Its significant role in the planet’s natural radioactivity is largely influenced by the long half-lives of its isotopes [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E]. Uranium’s abundance is approximately four parts per million (ppm), making it relatively common and widely distributed in the Earth’s crust [\u003Ca href=\"#B9\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E9\u003C\u002Fa\u003E]. Uranium is typically found in minerals, such as carnotite, uraninite, and autunite [\u003Ca href=\"#B9\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E9\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p7\"\u003EThe geological evolution of uranium, along with thorium, began approximately 4.5–3.5 billion years ago (Ga), a critical era in Earth’s history characterized by significant transformations within the planet’s crust [\u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E]. During this period, the Earth transitioned from its initial molten state to a more solidified form as it cooled. This cooling process led to the reduction of magmatic materials in the crust, which in turn facilitated the formation of early tetravalent actinide minerals. Notable among these early minerals are uraninite (UO\u003Csub\u003E2\u003C\u002Fsub\u003E), thorianite (ThO\u003Csub\u003E2\u003C\u002Fsub\u003E), and coffinite (USiO\u003Csub\u003E4\u003C\u002Fsub\u003E), which began to precipitate as the Earth’s crust began to solidify [\u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p8\"\u003EThese early minerals, in particular uraninite, are indicators of the redox conditions prevalent during the planet’s formative years. The oxidation states of uranium found in these minerals—such as IV\u003Csup\u003E4+\u003C\u002Fsup\u003E, V\u003Csup\u003E5+\u003C\u002Fsup\u003E, and VI\u003Csup\u003E6+\u003C\u002Fsup\u003E—reflect the changing environment conditions driven by interactions with microorganisms [\u003Ca href=\"#B10\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E10\u003C\u002Fa\u003E]. These interactions between geological and biological process not only influenced the mineral composition but also played a significant role in shaping oxidative states of uranium emerging from redox conditions of the time.\u003C\u002Fp\u003E\u003Cp id=\"p9\"\u003EContaining 92 protons, uranium is the element with the highest atomic number naturally occurring in the periodic table. The primary isotopes of uranium are Uranium-238 (U-238) with a half-life of 4.51 x 10\u003Csup\u003E9\u003C\u002Fsup\u003E years and Uranium-235 (U-235), with a half-life of 7.13 x 10\u003Csup\u003E8\u003C\u002Fsup\u003E years [\u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E]. These isotopes differ in the number of neutrons, affecting their stability and radioactivity. U-238 is the most abundant isotope, comprising about 99.3% of natural uranium, while U-235 accounts for approximately 0.7% [\u003Ca href=\"#B11\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E11\u003C\u002Fa\u003E]. Although these isotopes are chemically identical, they exhibit different behaviors in nuclear reactions. U-235, with 143 neutrons, is capable of undergoing fission when it absorbs a neutron, releasing energy in the process. In contrast, U-238, with 146 neutrons, absorbs a neutron to transform into Uranium-239. Uranium-239 subsequently undergoes two beta decays to become Plutonium-239, which is also a fissionable material [\u003Ca href=\"#B12\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E12\u003C\u002Fa\u003E]. The different nuclear behaviors of these isotopes play a significant role in their applications and the understanding of uranium’s role in natural radioactivity.\u003C\u002Fp\u003E\u003Cp id=\"p10\"\u003EBoth U-238 and U-235 isotopes are alpha emitters, meaning they emit alpha particles during radioactive decay [\u003Ca href=\"#B12\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E12\u003C\u002Fa\u003E]. The decay series of uranium ultimately result in stable, non-radioactive lead isotopes: Lead-206 (Pb-206) from U-238 and Lead-207 (Pb-207) from U-235 [\u003Ca href=\"#B12\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E12\u003C\u002Fa\u003E]. The alpha decay process involves the emission of helium nuclei (alpha particles), reducing the mass and atomic mass and atomic numbers of the parent isotopes, and is a critical aspect of uranium’s radioactivity [\u003Ca href=\"#B12\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E12\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p11\"\u003EUranium came into the spotlight with the discovery of nuclear fission in 1938 and subsequent demands of the nuclear industry [\u003Ca href=\"#B13\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E13\u003C\u002Fa\u003E]. Uranium has become, and remains, an ideal nuclear fuel due to its high density and excellent conductivity [\u003Ca href=\"#B13\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E13\u003C\u002Fa\u003E]. Controlling these properties was a key focus during the years 1943–1955, leading to worldwide efforts in several laboratories to separate single crystals of uranium to distinguish its intrinsic properties from extrinsic ones [\u003Ca href=\"#B13\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E13\u003C\u002Fa\u003E]. This challenge was ultimately met by the Argonne National Laboratory [ANL), demonstrating that uranium’s fundamental characteristics were indeed intrinsic [\u003Ca href=\"#B13\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E13\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p12\"\u003EIn conclusion, uranium’s role in natural radioactivity underscores its dual nature. The long half-lives of U-238 and U-235 contribute to the planet’s sustained natural radioactivity, influencing various geological and environmental processes, such as the generation of heat within the Earth’s crust and the radiometric dating of rock and minerals. Uranium’s radioactive decay is a key factor in understanding Earth’s geological history and the evolution of its crust.\u003C\u002Fp\u003E\u003Cp id=\"p13\"\u003EUranium’s duality is a product of its chemical consistency and its varied nuclear properties, alongside its significant roles in both geological and biological contexts. This duality illustrates the complex and multifaceted nature of uranium, encompassing its chemical uniformity, divergent nuclear behaviors, and influential interactions in natural systems.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_3\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E3. Uranium: From artistic medium to powerhouse of nuclear science\u003C\u002Fh2\u003E\u003Cp id=\"p14\"\u003EUranium has been used as a colorant in glass and ceramic glazes since ancient times, long before its radioactive properties were understood. Initially, uranium’s primary applications were artistic, particularly in glassmaking, ceramics, and glazes [\u003Ca href=\"#B14\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E14\u003C\u002Fa\u003E]. However, as scientific understanding advanced, uranium’s role extended far beyond esthetics. The groundwork for this transformation was laid by the French chemist Eugène-Melchior Péligot in 1841, when he first successfully isolated metallic uranium, marking a significant advancement in uranium chemistry [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E]. Péligot’s work transitioned uranium from a material prized for its decorative use to a substance with potential scientific significance, a potential that would soon be realized with the discovery of radioactivity.\u003C\u002Fp\u003E\u003Cp id=\"p15\"\u003EIn 1896, French physicist Henri Becquerel’s groundbreaking discovery of uranium’s natural radioactivity unveiled uranium’s true scientific importance [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E]. Becquerel observed that uranium salts emitted rays capable of exposing photographic plates, even in the absence of light [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E]. This discovery marked the beginning of a new era for uranium, connecting its earlier artistic applications to its pivotal role in the development of nuclear science. Uranium was no longer just a medium for vibrant glassware; it became a fundamental element in the understanding of atomic structure and the development of nuclear energy.\u003C\u002Fp\u003E\u003Cp id=\"p16\"\u003EThis discovery marked the birth of our understanding of radioactivity, a term later coined by Marie Curie. Curie, along with her husband Pierre, developed quantitative techniques to measure the radioactivity of uranium, further unraveling its mysterious nature. Through their meticulous research, they identified and isolated other radioactive elements within uranium ores, such as thorium, polonium, and radium, laying the foundation for modern nuclear science [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p17\"\u003EThe Curies’ recognition about the high radioactivity of uranium ores spurred further discoveries by radiochemists, leading to the identification of new radioactive elements and their chemical and nuclear compositions. The luminescent properties of radium created a demand for uranium ores in the medical field. It 1939, uranium became a central focus in the field of nuclear energy research following the discovery of nuclear fission by Otto Hahn and Fritz Strassman. The naturally occurring fissionable materials, such as Uranium-235, Uranium-238, and Uranium-233 (U-233), have since become of great scientific and technical importance in the pursuit of nuclear energy [\u003Ca href=\"#B8\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E8\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p18\"\u003EThe past and present applications of uranium highlight its dual nature: on one hand, a source of vivid color in artistic creations, and on the other, a powerful source of penetrating radiation that would revolutionize science and medicine. This duality, where uranium transitions from an esthetic material to a critical element in the study of atomic structure and energy, underscores its complex and multifaceted nature.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_4\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E4. Uranium applications\u003C\u002Fh2\u003E\u003Cp id=\"p19\"\u003EUranium’s diverse properties make it indispensable across a wide range of fields, from energy production to medical advancements and industrial processes. Its ability to undergo nuclear fission has made it a key component in clean energy alternatives, while its radioactive isotopes are crucial in medical diagnostics and treatments. Additionally, uranium plays a significant role in research and agricultural studies, underscoring its far-reaching impact. This section explores the various applications of uranium, highlighting its contributions to energy, medicine, and industry.\u003C\u002Fp\u003E\u003Cdiv class=\"section\" id=\"sec_4_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E4.1 Clean energy using uranium\u003C\u002Fh3\u003E\u003Cp id=\"p20\"\u003ENuclear energy is regarded as one of the safest and most sustainable methods for producing electricity, playing a critical role in the global transition to clean energy [\u003Ca href=\"#B15\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E15\u003C\u002Fa\u003E]. At the heart of nuclear power is uranium, the primary fuel of nuclear reactors [\u003Ca href=\"#B15\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E15\u003C\u002Fa\u003E]. Uranium’s unique properties, particularly the fissile U-235, make it the only naturally occurring element capable of sustaining a chain reaction necessary for nuclear fission [\u003Ca href=\"#B15\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E15\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p21\"\u003EThe potential of nuclear energy as a long-term renewable source is immense. It is estimated that with advancements in nuclear technology and more efficient fuel cycles, nuclear power could provide up to 9000 years of renewable energy [\u003Ca href=\"#B16\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E16\u003C\u002Fa\u003E]. This future includes the potential for reusing nuclear waste as fuel for advanced reactors, significantly reducing the overall waste produced by current nuclear technologies [\u003Ca href=\"#B16\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E16\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p22\"\u003EIn addition to reducing carbon emissions, nuclear energy offers a stable and reliable electricity source, as it is not dependent on weather conditions like solar or wind energy [\u003Ca href=\"#B17\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E17\u003C\u002Fa\u003E]. With ongoing innovations in nuclear technology, including next-generation reactors and improved safety protocols, uranium-based nuclear energy remains a key component in achieving global energy sustainability. This clean energy source has the potential to balance the growing demand for electricity [\u003Ca href=\"#B17\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E17\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_5_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E4.2 Uranium in medicine\u003C\u002Fh3\u003E\u003Cp id=\"p23\"\u003EUranium and its isotopes play a pivotal role in the field of nuclear medicine. Particularly, Uranium-230 (U-230) that has emerged along with Thorium-226 as critical elements in cancer therapy through their applications in “targeted alpha therapy” [\u003Ca href=\"#B18\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E18\u003C\u002Fa\u003E]. These isotopes decay by emitting alpha particles, which are highly effective in destroying cancer cells due to their high-energy and short-range penetration [\u003Ca href=\"#B19\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E19\u003C\u002Fa\u003E]. This makes them ideal for delivering precise and potent doses of radiation to tumors while minimizing damage to the surrounding healthy tissues [\u003Ca href=\"#B19\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E19\u003C\u002Fa\u003E, \u003Ca href=\"#B20\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E20\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p24\"\u003EUranium-230’s therapeutic potential extends beyond targeted alpha therapy. It serves as a valuable source to produce several important radionuclides, such Iodine-131, Molybdenum-99, Strontium-89, and Xenon-133 [\u003Ca href=\"#B21\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E21\u003C\u002Fa\u003E]. Iodine-131 is extensively used in the treatment of thyroid diseases, including thyroid cancer [\u003Ca href=\"#B22\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E22\u003C\u002Fa\u003E]. Molybdenum-99 is essential for generating Technetium-99 m (Tc-99 m), a widely employed diagnostic tool in medical imaging [\u003Ca href=\"#B23\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E23\u003C\u002Fa\u003E]. Strontium-89 has been utilized since 1993 to alleviate pain in patients with bone metastasis, [\u003Ca href=\"#B24\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E24\u003C\u002Fa\u003E] while Xenon-133 is used in lung imaging to aid in the diagnosis of respiratory conditions [\u003Ca href=\"#B25\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E25\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p25\"\u003EWhen combined with targeted delivery mechanisms, such as antibodies, these alpha-emitting isotopes can potentially offer a promising approach for treating challenging and resistant cancer type [\u003Ca href=\"#B19\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E19\u003C\u002Fa\u003E]. In clinical settings, the alpha particles emitted during decay of Uranium-230 and Thorium-226 provide substantial localized radiation that can more effectively destroy cancer cells compared to conventional beta or gamma radiation treatments [\u003Ca href=\"#B21\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E21\u003C\u002Fa\u003E]. These advancements are part of a broader initiative in nuclear medicine to develop more effective and less invasive cancer treatments, building on the unique radioactive properties of isotope like uranium.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_6_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E4.3 Uranium in industry\u003C\u002Fh3\u003E\u003Cp id=\"p26\"\u003EUranium’s versatility extends far beyond its well-known applications in medicine and energy; it also plays a significant role in various industrial processes due to its unique properties, which make it valuable in several sectors:\u003C\u002Fp\u003E\u003Cdiv class=\"section\" id=\"sec_6_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E4.3.1 Research and development\u003C\u002Fh4\u003E\u003Cp id=\"p27\"\u003EUranium is central in advancing research into nuclear science and materials. In particular, studies involving uranium have significantly contributed to our understanding of organo-actinide chemistry, which explores the bonding, reactivity, and molecular structures of uranium-containing organic compounds [\u003Ca href=\"#B26\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E26\u003C\u002Fa\u003E]. Research into uranium is essential to refining technologies related to nuclear energy and materials [\u003Ca href=\"#B27\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E27\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_7_3\" data-lvl=\"3\"\u003E\u003Ch4 class=\"heading subsection-title\"\u003E4.3.2 Agriculture\u003C\u002Fh4\u003E\u003Cp id=\"p28\"\u003EUranium has applications in agriculture, particularly in soil and water studies. Uranium isotopes, such as Uranium-238, can be used as tracers to study water movement [\u003Ca href=\"#B28\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E28\u003C\u002Fa\u003E, \u003Ca href=\"#B29\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E29\u003C\u002Fa\u003E]. Additionally, uranium’s radioactive properties can be employed to study the effects of uranium on plant growth [\u003Ca href=\"#B30\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E30\u003C\u002Fa\u003E] and fauna [\u003Ca href=\"#B31\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E31\u003C\u002Fa\u003E], examining potential effects on biodiversity and ecosystems.\u003C\u002Fp\u003E\u003Cp id=\"p29\"\u003EOverall, uranium’s role industry extends well beyond the nuclear sector, underscoring its diverse applications in research, agriculture, and environmental science.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_10\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E5. Uranium in the environment\u003C\u002Fh2\u003E\u003Cp id=\"p30\"\u003EWhile uranium is naturally present as a part of the Earth’s crust, its mobility in the environment is influenced by factors, such as pH levels, redox conditions, and the presence of other minerals and organic matter [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E]. These conditions can either immobilize uranium in sediments and soils or increase its solubility, allowing it to migrate into water systems [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E]. In aquatic environments, uranium can exist in both dissolved and particulate forms [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E]. Groundwater in certain regions, particularly those with uranium-rich geological formations, may exhibit elevated levels of uranium due to the natural leaching of the element from rocks [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p31\"\u003ETypically, concentrations of naturally occurring uranium that are found in the environment are low, posing minimal risk to human health under normal circumstances [\u003Ca href=\"#B32\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E32\u003C\u002Fa\u003E]. In the Earth’s crust, uranium concentration ranges from 1 to 4 mg\u002Fkg. Surface uranium strongly binds to oxygen forming hexavalent uranium (UO\u003Csub\u003E2\u003C\u002Fsub\u003E\u003Csup\u003E2+\u003C\u002Fsup\u003E), which is highly stable, soluble, and mobile [\u003Ca href=\"#B32\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E32\u003C\u002Fa\u003E]. Uranium can be detected in various water bodies, with concentrations in rivers, seawater, and groundwater typically being <4, 3.3, and < 5 μg\u002FL, respectively [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E]. In soils, uranium concentrations vary from 0.7 to 10.7 mg\u002Fkg [\u003Ca href=\"#B33\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E33\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p32\"\u003EHowever, uranium’s radioactive nature raises concerns about environmental contamination and health risks, particularly in areas affected by human activities, such as oil extraction, mining, nuclear energy production, and agriculture [\u003Ca href=\"#B34\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E34\u003C\u002Fa\u003E]. In these sectors, uranium can become more concentrated in waste products, increasing the risks of environmental contamination and public health hazards, if not properly managed [\u003Ca href=\"#B34\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E34\u003C\u002Fa\u003E]. The persistence of uranium in the environment, along with its radioactive decay products, necessitates careful monitoring and regulation to prevent harmful exposure and contamination [\u003Ca href=\"#B34\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E34\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p33\"\u003EUranium-238, a naturally occurring radioactive material (NORM), is particularly problematic in industries such as oil and gas, where extraction processes generate waste like sludge, scales, and produced water [\u003Ca href=\"#B35\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E35\u003C\u002Fa\u003E]. These byproducts contain radioactive elements, including uranium, which can contaminate soil, surface water, and groundwater [\u003Ca href=\"#B35\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E35\u003C\u002Fa\u003E]. In regions like the Permian Basin in the U.S., studies have shown elevated levels of uranium in groundwater near drilling sites, with uranium concentrations sometimes exceeding safe drinking water limits [\u003Ca href=\"#B36\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E36\u003C\u002Fa\u003E]. These contaminants pose long-term risks, as the radioisotopes from uranium have half-lives extending millions of years, contributing to persistent environmental hazards [\u003Ca href=\"#B36\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E36\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p34\"\u003EUranium mining, the first step in nuclear power generation, also poses significant environmental and health risks [\u003Ca href=\"#B37\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E37\u003C\u002Fa\u003E]. Mining operations generate dust and use large volumes of water for dust control and uranium extraction, both of which can spread long-lived radioisotopes into the surrounding environment [\u003Ca href=\"#B37\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E37\u003C\u002Fa\u003E]. Dust particles containing uranium and its decay products can be inhaled, ingested, or absorbed through the skin [\u003Ca href=\"#B38\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E38\u003C\u002Fa\u003E]. Gamma-ray emissions from radioactive materials present in mining waste further elevate exposure risks, particularly for workers [\u003Ca href=\"#B38\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E38\u003C\u002Fa\u003E]. Occupational exposure in mining regions, such as in Namibia, has been linked to increased cases of lung cancer and other radiation-induced illnesses [\u003Ca href=\"#B39\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E39\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p35\"\u003ETo illustrate the scale of uranium’s environmental impact, a case study from the Navajo Nation in the U.S. provides a sobering example [\u003Ca href=\"#B40\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E40\u003C\u002Fa\u003E]. Over 500 abandoned uranium mines have contaminated local water supplies, leading to uranium concentrations in excess of the U.S. Environmental Protection Agency’s (EPA’s) 30 μg\u002FL drinking water limit [\u003Ca href=\"#B41\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E41\u003C\u002Fa\u003E]. As a result, there has been a documented increase in health complications among residents, including kidney disease and cancer [\u003Ca href=\"#B38\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E38\u003C\u002Fa\u003E]. This highlights the profound and complex health implications of uranium exposure, especially in communities living near mining operations.\u003C\u002Fp\u003E\u003Cp id=\"p36\"\u003ERecent research into uranium’s environmental effects has revealed long-term contamination pathways, including groundwater transport, soil accumulation, and bioaccumulation in plants and animals [\u003Ca href=\"#B38\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E38\u003C\u002Fa\u003E]. Once mobilized into water systems, uranium contamination can spread across vast distances, potentially impacting downstream ecosystems and human populations [\u003Ca href=\"#B7\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E7\u003C\u002Fa\u003E, \u003Ca href=\"#B38\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E38\u003C\u002Fa\u003E]. Furthermore, phosphate fertilizers, a significant source of uranium contamination, exacerbate these issues. In countries like Brazil, uranium concentrations in fertilizers have been recorded at levels ranging from 5.17 to 54.3 μg\u002Fg, which pose a substantial risk for groundwater contamination [\u003Ca href=\"#B2\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E2\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p37\"\u003EAddressing these challenges requires a multifaceted approach, including advancements in remediation technologies. Emerging techniques, such as bioremediation, where microbes are used to immobilize uranium in contaminated soils and water, have shown promise [\u003Ca href=\"#B42\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E42\u003C\u002Fa\u003E]. Current research is focusing on remediation strategies, which leverage microbial processes to immobilize uranium and use electrochemical methods and adsorbent materials that can capture and remove uranium from contaminated water [\u003Ca href=\"#B43\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E43\u003C\u002Fa\u003E, \u003Ca href=\"#B44\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E44\u003C\u002Fa\u003E, \u003Ca href=\"#B45\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E45\u003C\u002Fa\u003E, \u003Ca href=\"#B46\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E46\u003C\u002Fa\u003E, \u003Ca href=\"#B47\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E47\u003C\u002Fa\u003E]. Additionally, new adsorbent materials, like modified biochars [\u003Ca href=\"#B48\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E48\u003C\u002Fa\u003E] and metal-organic frameworks (MOFs) [\u003Ca href=\"#B49\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E49\u003C\u002Fa\u003E], are being explored to efficiently remove uranium from contaminated water. These innovative strategies offer hope for managing uranium’s environmental footprint more effectively.\u003C\u002Fp\u003E\u003Cp id=\"p38\"\u003EIn conclusion, uranium embodies a duality of immense potential and significant risk. Its role in nuclear energy underscores its values, but the environmental and health risks associated with its radioactive nature and industrial activities demand vigilant management. The balance between harnessing uranium’s benefits and mitigating its dangers remains a critical challenge for the future.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_11\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E6. Uranium demand and economy\u003C\u002Fh2\u003E\u003Cp id=\"p39\"\u003EUranium, with its exceptional energy potential, lies at the heart of one of the most powerful energy sources: nuclear power. As countries move toward adopting sustainable energy solutions and committing to carbon-free emissions, the demand for uranium remains fundamental fuel that powers nuclear reactors.\u003C\u002Fp\u003E\u003Cdiv class=\"section\" id=\"sec_11_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E6.1 Uranium demand in nuclear energy\u003C\u002Fh3\u003E\u003Cp id=\"p40\"\u003EThe demand for uranium is mainly determined by its use in nuclear reactors. In 2020, several countries relied heavily on uranium-based nuclear energy, with France generating 69.11%, Sweden 31.24%, and United States 18.72% of their electricity from nuclear power plants [\u003Ca href=\"#B47\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E47\u003C\u002Fa\u003E]. As of 2023, there were approximately 450 nuclear reactors operating globally, supplying approximately 10% of the world’s electricity [\u003Ca href=\"#B50\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E50\u003C\u002Fa\u003E]. Major uranium consumers included the United States, France, China, and Russia, as these countries depended significantly on nuclear power for their electricity generation needs [\u003Ca href=\"#B50\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E50\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p41\"\u003EThe International Energy Agency (IEA) projects that global uranium consumption will rise by 39% by 2050 as nuclear energy continues to be integrated into low-carbon energy strategies [\u003Ca href=\"#B51\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E51\u003C\u002Fa\u003E]. This surge is driven by the increasing global demand for electricity and the need to meet climate goals while reducing greenhouse gas emissions from fossil fuels [\u003Ca href=\"#B51\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E51\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_12_2\" data-lvl=\"2\"\u003E\u003Ch3 class=\"heading section-title\"\u003E6.2 Geopolitical and economic influences on uranium demand\u003C\u002Fh3\u003E\u003Cp id=\"p42\"\u003EGeopolitical factors also play a crucial role in shaping uranium demand. In response to the growing urgency of climate change, countries like the United States have committed to reduce reliance on fossil fuels. Legislation efforts are underway to develop the next generation of nuclear power plants, further boosting uranium demand [\u003Ca href=\"#B51\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E51\u003C\u002Fa\u003E]. This shift toward nuclear energy, however, brings with it challenges related to the environmental agreement.\u003C\u002Fp\u003E\u003Cp id=\"p43\"\u003EHistorically, the uranium industry has contributed to significant environmental pollution, especially in regions where mining has been extensive [\u003Ca href=\"#B52\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E52\u003C\u002Fa\u003E]. New legislation in the United States seeks to balance the need for uranium with environmental stewardship by exploring the opening of new mines and the potential reopening of old ones [\u003Ca href=\"#B52\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E52\u003C\u002Fa\u003E]. Despite these initiatives, ongoing pollution issues persist, particularly in states like Arizona and New Mexico, which have historically supplied much of the country’s uranium [\u003Ca href=\"#B52\" class=\"ref-link\" data-ref-style=\"bibr\"\u003E52\u003C\u002Fa\u003E].\u003C\u002Fp\u003E\u003Cp id=\"p44\"\u003EThe challenge moving forward lies in balancing uranium’s critical role in reducing carbon emissions with environmental and ethical responsibilities that come with its extraction and use. As the demand for uranium rises alongside the global transition to sustainable energy, efforts to minimize its environmental impact and ensure safe, regulated use will become more crucial.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_14\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003E7. Conclusion\u003C\u002Fh2\u003E\u003Cp id=\"p45\"\u003EUranium remains a critical resource, essential not only for energy generation but also for its applications in technological advancements across industry, research, and medicine. Its role in the global energy landscape is complex and multifaceted. On one hand, uranium fuels nuclear reactors, providing a low-carbon energy source that helps to meet the rising global demand for electricity. On the other hand, its extraction, radioactive properties, and waste management pose significant environmental and health risks, raising important concerns about the sustainability and safety of its continued use.\u003C\u002Fp\u003E\u003Cp id=\"p46\"\u003EAs the global energy transition unfolds, the duality of uranium—as both a valuable source and a potential hazard—will become even more pronounced. The future of uranium demand will depend on how the world balances the need for clean energy with the imperative of minimizing environmental and public health risks. Sustainable mining practices, innovative nuclear technologies, and international cooperation will be key to navigating the challenges and opportunities associated with uranium in the twenty-first century. By navigating this delicate balance, we can harness uranium’s potential while mitigating its dangers, ensuring that its dual nature is managed responsibly for future generations.\u003C\u002Fp\u003E\u003Cp id=\"p47\"\u003ELooking ahead, technological advancements in nuclear waste management, such as more efficient containment systems and recycling methods, will be critical to minimizing uranium’s environmental footprint. Additionally, research into alternative energy systems may provide new pathways to harnessing nuclear power while reducing dependency on traditional uranium-based technologies.\u003C\u002Fp\u003E\u003Cp id=\"p48\"\u003EIn conclusion, uranium’s dual role as both a key resource and a potential hazard must be managed responsibly. By adopting forward-looking strategies and fostering international collaboration, we can harness uranium’s potential while mitigating its dangers, ensuring that future generations can benefit from its energy potential without compromising environmental and public health.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_15\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003EAcknowledgments\u003C\u002Fh2\u003E\u003Cp id=\"p49\"\u003EThe authors would like to acknowledge the Department of Energy-National Nuclear Security Administration-Minority Serving Institution Partnership Program (MSIPP) Scholarly Partnership in Nuclear Security (SPINS) Consortium, Grant number DE-NA0003980, and Graduate Research Training Initiative for Student Enhancement (G-RISE) program at the University of Texas at El Paso, Grant number: 5T32GM144919-03.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"section\" id=\"sec_18\" data-lvl=\"1\"\u003E\u003Ch2 class=\"heading main-title\"\u003EConflict of interest\u003C\u002Fh2\u003E\u003Cp id=\"p50\"\u003EThe authors declare no conflict of interest.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\n","keywords":"uranium,use of uranium,duality,environment,health effects","chapterPDFUrl":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa043Y000011YN3CQAW\u002Fa09Tc000001BC25IAG\u002FFinal-Perspective%20Chapter%3A%20The%20dual%20nature%20and%20applicati%20%282024-10-18%2018%3A03%3A44%29.pdf","chapterXML":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa043Y000011YN3CQAW\u002Fa09Tc000001BC25IAG\u002FFinal%20%28xml%29-Perspective%20Chapter%3A%20The%20dual%20nature%20and%20applicati%20%282024-10-18%2020%3A53%3A53%29.xml","webChapterXML":"s3:\u002F\u002Fintech-chapter-xmls\u002Fxmls-chapter\u002F1202198\u002F1730303850-1603569441\u002F","downloadPdfUrl":"\u002Fchapter\u002Fpdf-download\u002F1202198","previewPdfUrl":"\u002Fchapter\u002Fpdf-preview\u002F1202198","cdnMediaBaseUrl":null,"totalDownloads":17,"totalViews":0,"totalCrossrefCites":0,"totalDimensionsCites":0,"dateSubmitted":"September 9th 2024","dateReviewed":"September 14th 2024","datePrePublished":"October 21st 2024","datePublished":null,"dateFinished":null,"readingETA":"0","abstract":"\u003Cp id=\"p1\"\u003EUranium is a unique element, characterized by its dual role as a valuable resource and a source of significant hazards. Widely used in industry, research, and medicine, uranium has played a pivotal role in shaping modern science and technology. Since the discovery of its fission properties in the early twentieth century, uranium has gained attention as a powerful and influential element. Historically, uranium’s role in the discovery of radioactivity marked a turning point in scientific research, and its ability to release immense energy through nuclear fission has transformed human history. From its destructive potential in warfare to its peaceful applications in electricity generation via nuclear power plants, uranium has had a profound impact. Furthermore, it has advanced medical science through the production of isotopes for diagnostic imaging and therapeutic treatments. However, increased demand for uranium has led to expanded mining and milling processes, which pose public health risks due to environmental contamination. This chapter explores uranium’s legacy, highlighting its scientific significance while balancing the potential benefits with the inherent risks associated with its use. The discussion underscores the need for careful consideration and management of uranium’s dual nature as both a powerful resource and potential source of harm.\u003C\u002Fp\u003E\n","reviewType":"peer-reviewed","bibtexUrl":"\u002Fchapter\u002Fbibtex\u002F1202198","risUrl":"\u002Fchapter\u002Fris\u002F1202198","signatures":"Angelica A. Chacon and Carlos R. Cabrera","isPublished":false,"isOnlineFirst":true,"isDeactivated":0,"noAds":0,"subseries":null,"book":{"id":"1003971","type":"book","title":"Heavy Metals in the Environment","subtitle":null,"fullTitle":"Heavy Metals in the Environment","slug":null,"isPublished":false,"publishedDate":null,"bookSignature":"Dr. Mitsuo Yoshida","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa043Y000011YN3CQAW\u002F0015875_TrikoderCover%20%282023-10-29%2016%3A53%3A59%29.jpg","cdnCoverURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1003971\u002F1713449943-1735544242\u002Fcover.jpg","cdnCoverURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1003971\u002F1713449943-1735544242\u002Fcover-300.jpg","cdnWebCoverURL":null,"cdnWebCoverURL300":null,"cdnCoverWithTextURL":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1003971\u002F1718124913-401327236\u002Fcover-text.jpg","cdnCoverWithTextURL300":"https:\u002F\u002Fcdnintech.com\u002Fbooks\u002F1003971\u002F1718124913-401327236\u002Fcover-text-300.jpg","licenceType":"CC BY 4.0","editedByType":null,"isbn":"978-0-85014-846-6","printIsbn":"978-0-85014-847-3","pdfIsbn":"978-0-85014-848-0","isAvailableForWebshopOrdering":true,"isDeactivated":false,"kuFlag":false,"noAdsSub":0,"editors":[{"id":"436806","title":"Dr.","name":"Mitsuo","middleName":null,"surname":"Yoshida","slug":"mitsuo-yoshida","fullName":"Mitsuo Yoshida"}],"productType":{"id":"1","title":"Edited Volume","chapterContentType":"chapter","authoredCaption":"Edited by"}},"authors":[{"id":"605653","title":"M.Sc.","name":"Angelica A.","middleName":null,"surname":"Chacon","fullName":"Angelica A. Chacon","slug":"angelica-a.-chacon","email":"aachacon3@miners.utep.edu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","institution":null},{"id":"605664","title":"Dr.","name":"Carlos R.","middleName":null,"surname":"Cabrera","fullName":"Carlos R. Cabrera","slug":"carlos-r.-cabrera","email":"crcabrerama@utep.edu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","institution":{"name":"The University of Texas at El Paso","institutionURL":null,"country":{"name":"United States of America"}}}],"sections":[{"id":"sec_1","title":"1. Introduction","level":"1"},{"id":"sec_2","title":"2. Uranium in nature and its evolution","level":"1"},{"id":"sec_3","title":"3. Uranium: From artistic medium to powerhouse of nuclear science","level":"1"},{"id":"sec_4","title":"4. Uranium applications","level":"1"},{"id":"sec_4_2","title":"4.1 Clean energy using uranium","level":"2"},{"id":"sec_5_2","title":"4.2 Uranium in medicine","level":"2"},{"id":"sec_6_2","title":"4.3 Uranium in industry","level":"2"},{"id":"sec_6_3","title":"4.3.1 Research and development","level":"3"},{"id":"sec_7_3","title":"4.3.2 Agriculture","level":"3"},{"id":"sec_10","title":"5. Uranium in the environment","level":"1"},{"id":"sec_11","title":"6. Uranium demand and economy","level":"1"},{"id":"sec_11_2","title":"6.1 Uranium demand in nuclear energy","level":"2"},{"id":"sec_12_2","title":"6.2 Geopolitical and economic influences on uranium demand","level":"2"},{"id":"sec_14","title":"7. Conclusion","level":"1"},{"id":"sec_15","title":"Acknowledgments","level":"1"},{"id":"sec_18","title":"Conflict of interest","level":"1"}],"chapterReferences":[{"id":"B1","body":"\u003Cref id=\"B1\"\u003E\u003Cmixed-citation publication-type=\"other\"\u003EU.S Department of Energy Office of Nuclear Energy. Nuclear Energy Facts: Uranium. Available from: \u003Cext-link ext-link-type=\"uri\" xlink:href=\"https:\u002F\u002Fwww.energy.gov\u002Fne\u002Fnuclear-fuel-facts-uranium\"\u003Ehttps:\u002F\u002Fwww.energy.gov\u002Fne\u002Fnuclear-fuel-facts-uranium\u003C\u002Fext-link\u003E\u003C\u002Fmixed-citation\u003E\u003C\u002Fref\u003E"},{"id":"B2","body":"\u003Cref id=\"B2\"\u003E\u003Cmixed-citation publication-type=\"journal\"\u003EBalaram V, Rani A, Rathore DPS. Uranium in groundwater in parts of India and world: A comprehensive review of sources, impact to the environment and human health, analytical techniques, and mitigation technologies. 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Available from: \u003Cext-link ext-link-type=\"uri\" xlink:href=\"https:\u002F\u002Fe360.yale.edu\u002Ffeatures\u002Fus-uranium-mining-nuclear-power\"\u003Ehttps:\u002F\u002Fe360.yale.edu\u002Ffeatures\u002Fus-uranium-mining-nuclear-power\u003C\u002Fext-link\u003E\u003C\u002Fmixed-citation\u003E\u003C\u002Fref\u003E"}],"footnotes":[],"contributors":[{"corresp":"yes","contributorFullName":"Angelica A. Chacon","address":"aachacon3@miners.utep.edu","affiliation":"\u003Cul class=\"list\"\u003E\u003Cli\u003EThe University of Texas at El Paso, El Paso, Texas, United States\u003C\u002Fli\u003E\u003C\u002Ful\u003E"},{"corresp":null,"contributorFullName":"Carlos R. 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Residents of European Union countries need to add VAT based on the specific rate applied in their country of residence. Institutions and companies registered as VAT taxable entities in their own EU member state will not pay VAT by providing us with their VAT registration number. This is made possible by the EU reverse charge method.\u003C\u002Fem\u003E\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Cstrong\u003E\u003Cem\u003EOptional Production Services\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EStraive is our official partner for Copyediting and Typesetting. Unlike other publishers we provide authors with full XML Typesetting, English language copyediting & proofreading services at no extra charge.\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EIn addition to these services, IntechOpen Authors can access a range of additional professional pre-submission editorial services offered by Straive through their AuthorMate platform at a discounted price. 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Their services are designed to convey the essence of your work to readers from across the globe in the language they understand. IntechOpen Authors that wish to use this service before submission will receive a 20% discount on all translation services. To find out more information or obtain a quote, please visit \u003Ca href=\\\"https:\u002F\u002Fwww.enago.com\u002Fintech\\\"\u003Ehttps:\u002F\u002Fwww.enago.com\u002Fintech\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Cstrong\u003EFUNDING\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EWe feel that financial barriers should never prevent researchers from publishing their work. Please consult our \u003Ca href=\\\"\u002Fpage\u002Fopen-access-funding\\\"\u003EOpen Access Funding page\u003C\u002Fa\u003E to explore funding opportunities and learn more about how you can finance your IntechOpen publication.\u003C\u002Fp\u003E\\n\\n\u003Cp\u003E\u003Cstrong\u003EBENEFITS\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\\n\\n\u003Cul\u003E\\n\\t\u003Cli\u003EYour published content is immediately available to read, share and download for free\u003C\u002Fli\u003E\\n\\t\u003Cli\u003E+3.3 million unique visitors per month\u003C\u002Fli\u003E\\n\\t\u003Cli\u003E+184,650 Web Of Science citations\u003C\u002Fli\u003E\\n\\t\u003Cli\u003EYou retain copyright to your work\u003C\u002Fli\u003E\\n\\t\u003Cli\u003EChapter and book statistics performance reports allowing you to examine the reach of your content\u003C\u002Fli\u003E\\n\\t\u003Cli\u003EFull PDF version of your book available to download\u003C\u002Fli\u003E\\n\\t\u003Cli\u003ERapid publishing process with personal support\u003C\u002Fli\u003E\\n\\t\u003Cli\u003ECompetitive pricing for publishing services and print products\u003C\u002Fli\u003E\\n\u003C\u002Ful\u003E\\n\\n\u003Cp\u003E\u003Cstrong\u003ESEND YOUR PROPOSAL\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\\n\\n\u003Cp\u003EIf you are interested in publishing your book with IntechOpen, please submit your book proposal by completing the \u003Ca href=\\\"https:\u002F\u002Fwww.intechopen.com\u002Fpublishing-proposal\\\"\u003EPublishing Proposal Form\u003C\u002Fa\u003E. \u003C\u002Fp\u003E\\n\\n\u003Cp\u003ENot sure if this is the right option for you? 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Their services are designed to convey the essence of your work to readers from across the globe in the language they understand. IntechOpen Authors that wish to use this service before submission will receive a 20% discount on all translation services. To find out more information or obtain a quote, please visit \u003Ca href=\"https:\u002F\u002Fwww.enago.com\u002Fintech\"\u003Ehttps:\u002F\u002Fwww.enago.com\u002Fintech\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\n\n\u003Cp\u003E\u003Cstrong\u003EFUNDING\u003C\u002Fstrong\u003E\u003C\u002Fp\u003E\n\n\u003Cp\u003EWe feel that financial barriers should never prevent researchers from publishing their work. 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Please refer back to the main \u003Ca href=\"\u002Fpublish\"\u003EPublish with IntechOpen page\u003C\u002Fa\u003E or feel free to contact us directly at \u003Ca href=\"http:\u002F\u002Fbook.department@intechopen.com\"\u003Ebook.department@intechopen.com\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\n"}]},"successStories":{"items":[]},"authorsAndEditors":{"filterParams":{"sort":"featured,name"},"profiles":[],"filtersByRegion":[],"offset":0,"limit":12,"total":null},"chapterEmbeded":{"data":{}},"editorApplication":{"success":null,"errors":{}},"ofsBooks":{"filterParams":{},"books":[],"filtersByTopic":[],"offset":0,"limit":12,"total":null},"ofsBookV4":{"item":{"type":"book","id":"1004431","leadTitle":null,"title":"Understanding Sexually Transmitted Diseases - Prevention, Symptoms, and Treatment Options\u003Cbr\u003E","subtitle":null,"reviewType":"peer-reviewed","abstract":"Sexually transmitted diseases (STDs) remain among the most significant global health problems, affecting several people annually and often affecting practically all populations. 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Generally, the phytochemical constituents of plants fall into two categories based on their role in basic metabolic processes, namely primary and secondary metabolites. Primary plant metabolites are involved in basic life functions; therefore, they are more or less similar in all living cells. On the other hand, secondary plant metabolites are products of subsidiary pathways as the shikimic acid pathway. In the course of studying, the medicinal effect of herbals is oriented towards the secondary plant metabolites. Secondary plant metabolites played an important role in alleviating several aliments in the traditional medicine and folk uses. In modern medicine, they provided lead compounds for the production of medications for treating various diseases from migraine up to cancer. Secondary plant metabolites are classified according to their chemical structures into various classes. 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Illness is regarded as having both natural and supernatural causes and thus must be treated by both physical and spiritual means, using divination, incantations, animal sacrifice, exorcism, and herbs. Herbal medicine is the cornerstone of traditional medicine but may include minerals and animal parts. The adjustment is ok, but may be replaced with –‘ Herbal medicine was once termed primitive by western medicine but through scientific investigations there is a better understanding of its therapeutic activities such that many pharmaceuticals have been modeled on phytochemicals derived from it. Major obstacles to the use of African medicinal plants are their poor quality control and safety. Traditional medical practices are still shrouded with much secrecy, with few reports or documentations of adverse reactions. 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Formal recognition and integration of traditional medicine into conventional medicine will hold much promise for the future.","isPublished":true,"isOnlineFirst":false,"book":{"id":"6302","slug":"herbal-medicine","title":"Herbal Medicine","fullTitle":"Herbal Medicine","isOpenForSubmission":false,"isPublished":true},"signatures":"Ezekwesili-Ofili Josephine Ozioma and Okaka Antoinette Nwamaka\nChinwe","authors":[{"id":"191264","title":"Prof.","name":"Josephine","middleName":"Ozioma","surname":"Ozioma Ezekwesili-Ofili","slug":"josephine-ozioma-ezekwesili-ofili","fullName":"Josephine Ozioma Ezekwesili-Ofili"},{"id":"211585","title":"Prof.","name":"Antoinette","middleName":null,"surname":"Okaka","slug":"antoinette-okaka","fullName":"Antoinette Okaka"}]},{"id":"58270","doi":"10.5772\u002Fintechopen.72437","title":"Toxicity and Safety Implications of Herbal Medicines Used in Africa","slug":"toxicity-and-safety-implications-of-herbal-medicines-used-in-africa","totalDownloads":4385,"totalCrossrefCites":42,"totalDimensionsCites":110,"abstract":"The use of herbal medicines has seen a great upsurge globally. In developing countries, many patronize them largely due to cultural acceptability, availability and cost. In developed countries, they are used because they are natural and therefore assumed to be safer than allopathic medicines. In recent times, however, there has been a growing concern about their safety. This has created a situation of ambivalence in discussions regarding their use. Some medicinal plants are intrinsically toxic by virtue of their constituents and can cause adverse reactions if inappropriately used. Other factors such as herb-drug interactions, lack of adherence to good manufacturing practice (GMP), poor regulatory measures and adulteration may also lead to adverse events in their use. Many in vivo tests on aqueous extracts largely support the safety of herbal medicines, whereas most in vitro tests on isolated single cells mostly with extracts other than aqueous ones show contrary results and thus continue the debate on herbal medicine safety. It is expected that toxicity studies concerning herbal medicine should reflect their traditional use to allow for rational discussions regarding their safety for their beneficial use. While various attempts continue to establish the safety of various herbal medicines in man, their cautious and responsible use is required.","isPublished":true,"isOnlineFirst":false,"book":{"id":"6302","slug":"herbal-medicine","title":"Herbal Medicine","fullTitle":"Herbal Medicine","isOpenForSubmission":false,"isPublished":true},"signatures":"Merlin L.K. Mensah, Gustav Komlaga, Arnold D. Forkuo, Caleb\nFirempong, Alexander K. Anning and Rita A. 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Furthermore, it is well documented that the essential oil and extracts of Mentha species possess antimicrobial, fungicidal, antiviral, insecticidal, and antioxidant properties. The economic importance of mints is also evident; mint oil and its constituents and derivatives are used as flavoring agents throughout the world in food, pharmaceutical, herbal, perfumery, and flavoring industry. To provide a scientific basis for their traditional uses, several studies have been conducted to determine the chemical composition of mints and assess their biological activities. This chapter describes the therapeutic effects and uses of Mentha species and their constituents, particularly essential oils and phenolic compounds; some additional biological activities will also be considered.","isPublished":true,"isOnlineFirst":false,"book":{"id":"5612","slug":"aromatic-and-medicinal-plants-back-to-nature","title":"Aromatic and Medicinal Plants","fullTitle":"Aromatic and Medicinal Plants - Back to Nature","isOpenForSubmission":false,"isPublished":true},"signatures":"Fatiha Brahmi, Madani Khodir, Chibane Mohamed and Duez Pierre","authors":[{"id":"193281","title":"Dr.","name":"Fatiha","middleName":null,"surname":"Brahmi","slug":"fatiha-brahmi","fullName":"Fatiha Brahmi"},{"id":"199693","title":"Prof.","name":"Khodir","middleName":null,"surname":"Madani","slug":"khodir-madani","fullName":"Khodir Madani"},{"id":"199694","title":"Prof.","name":"Pierre","middleName":null,"surname":"Duez","slug":"pierre-duez","fullName":"Pierre Duez"},{"id":"203738","title":"Prof.","name":"Mohamed","middleName":null,"surname":"Chibane","slug":"mohamed-chibane","fullName":"Mohamed Chibane"}]},{"id":"77433","doi":"10.5772\u002Fintechopen.98602","title":"Extraction of Bioactive Compounds from Medicinal Plants and Herbs","slug":"extraction-of-bioactive-compounds-from-medicinal-plants-and-herbs","totalDownloads":7497,"totalCrossrefCites":35,"totalDimensionsCites":86,"abstract":"Human beings have relied on herbs and medicinal plants as sources of food and remedy from time immemorial. Bioactive compounds from plants are currently the subject of much research interest, but their extraction as part of phytochemical and\u002For biological investigations present specific challenges. Herbalists or scientists have developed many protocols of extraction of bioactive ingredients to ensure the effectiveness and the efficacy of crude drugs that were used to get relief from sickness. With the advent of new leads from plants such as morphine, quinine, taxol, artemisinin, and alkaloids from Voacanga species, a lot of attention is paid to the mode of extraction of active phytochemicals to limit the cost linked to the synthesis and isolation. Thus, the extraction of active compounds from plants needs appropriate extraction methods and techniques that provide bioactive ingredients-rich extracts and fractions. The extraction procedures, therefore, play a critical role in the yield, the nature of phytochemical content, etc. This chapter aims to present, describe, and compare extraction procedures of bioactive compounds from herbs and medicinal plants.","isPublished":true,"isOnlineFirst":false,"book":{"id":"10356","slug":"natural-medicinal-plants","title":"Natural Medicinal Plants","fullTitle":"Natural Medicinal Plants","isOpenForSubmission":false,"isPublished":true},"signatures":"Yannick Stéphane Fongang Fotsing, Jean Jules Bankeu Kezetas, Gaber El-Saber Batiha, Iftikhar Ali and Bruno Lenta Ndjakou","authors":[{"id":"224515","title":"Dr.","name":"Fongang Fotsing","middleName":null,"surname":"Yannick Stéphane","slug":"fongang-fotsing-yannick-stephane","fullName":"Fongang Fotsing Yannick Stéphane"},{"id":"227816","title":"Dr.","name":"Bankeu Kezetas","middleName":null,"surname":"Jean Jules","slug":"bankeu-kezetas-jean-jules","fullName":"Bankeu Kezetas Jean Jules"},{"id":"227817","title":"Prof.","name":"Lenta Ndjakou","middleName":null,"surname":"Bruno","slug":"lenta-ndjakou-bruno","fullName":"Lenta Ndjakou Bruno"},{"id":"349790","title":"Prof.","name":"Gaber","middleName":null,"surname":"El-Saber Batiha","slug":"gaber-el-saber-batiha","fullName":"Gaber El-Saber Batiha"},{"id":"357350","title":"Dr.","name":"Iftikhar","middleName":null,"surname":"Ali","slug":"iftikhar-ali","fullName":"Iftikhar Ali"}]}],"mostDownloadedChaptersLast30Days":[{"id":"23463","title":"Method Development and Validation of Analytical Procedures","slug":"method-development-and-validation-of-analytical-procedures","totalDownloads":32282,"totalCrossrefCites":7,"totalDimensionsCites":13,"abstract":null,"isPublished":true,"isOnlineFirst":false,"book":{"id":"631","slug":"quality-control-of-herbal-medicines-and-related-areas","title":"Quality Control of Herbal Medicines and Related Areas","fullTitle":"Quality Control of Herbal Medicines and Related Areas","isOpenForSubmission":false,"isPublished":true},"signatures":"Kapil Kalra","authors":[{"id":"36680","title":"Dr.","name":"Kapil","middleName":null,"surname":"Kalra","slug":"kapil-kalra","fullName":"Kapil Kalra"}]},{"id":"77433","title":"Extraction of Bioactive Compounds from Medicinal Plants and Herbs","slug":"extraction-of-bioactive-compounds-from-medicinal-plants-and-herbs","totalDownloads":7480,"totalCrossrefCites":35,"totalDimensionsCites":86,"abstract":"Human beings have relied on herbs and medicinal plants as sources of food and remedy from time immemorial. Bioactive compounds from plants are currently the subject of much research interest, but their extraction as part of phytochemical and\u002For biological investigations present specific challenges. Herbalists or scientists have developed many protocols of extraction of bioactive ingredients to ensure the effectiveness and the efficacy of crude drugs that were used to get relief from sickness. With the advent of new leads from plants such as morphine, quinine, taxol, artemisinin, and alkaloids from Voacanga species, a lot of attention is paid to the mode of extraction of active phytochemicals to limit the cost linked to the synthesis and isolation. Thus, the extraction of active compounds from plants needs appropriate extraction methods and techniques that provide bioactive ingredients-rich extracts and fractions. 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Consumers prefer minimally processed pomegranate arils and frozen arils packed in punnets over whole fruit. Juices can be used in beverages and for various treatment purposes. This new sector of pomegranate processing will allow the use of non-commercial pomegranate fruits and improve pomegranate utilization for human health.","isPublished":true,"isOnlineFirst":false,"book":{"id":"10171","slug":"pomegranate","title":"Pomegranate","fullTitle":"Pomegranate","isOpenForSubmission":false,"isPublished":true},"signatures":"Sangram S. Dhumal, Ravindra D. Pawar and Sandip S. Patil","authors":[{"id":"209772","title":"Dr.","name":"Sangram S.","middleName":"Sahebrao","surname":"Dhumal","slug":"sangram-s.-dhumal","fullName":"Sangram S. Dhumal"},{"id":"454539","title":"Dr.","name":"Ravindra D.","middleName":null,"surname":"Pawar","slug":"ravindra-d.-pawar","fullName":"Ravindra D. 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The adjustment is ok, but may be replaced with –‘ Herbal medicine was once termed primitive by western medicine but through scientific investigations there is a better understanding of its therapeutic activities such that many pharmaceuticals have been modeled on phytochemicals derived from it. Major obstacles to the use of African medicinal plants are their poor quality control and safety. Traditional medical practices are still shrouded with much secrecy, with few reports or documentations of adverse reactions. However, the future of African traditional medicine is bright if viewed in the context of service provision, increase of health care coverage, economic potential, and poverty reduction. 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He has over 30 years of academic and research experience in different international universities. He has also worked in the industry as Manager Research and Development, Deputy Manager Design, Production Engineer, and Quality Control Engineer. He has been actively involved in research and accreditation work related to engineering education. His research areas are Applied materials and Applied materials and manufacturing; Applied mechanics and design; Reliability engineering; Analytical, numerical, and stochastic modeling; Development of experimental facilities; Metalforming (extrusion) process, dies and tools, and product defects; Expandable and other specialty steels; Swelling elastomers and novel polymers for oil and gas industry; Sustainable engineering; manufacturing; Applied mechanics and design; Reliability engineering; and Engineering education. As part of the Applied Mechanics and Advanced Materials Research group (AM2R) at SQU, he has been involved in different applied research funded projects in excess of 4 million dollars. He has over 230 research\u002Ftechnical publications to his credit (research monographs\u002Fbooks, edited book volumes, book chapters, publications in refereed international journals and conferences, and technical reports). His recent books include Swelling Elastomers in Petroleum Drilling and Development — Applications, Performance Analysis, and Material Modeling; the volume on Renewability of Synthetic Materials in Elsevier Encyclopedia of Renewable and Sustainable Materials; the volume Thermal Engineering of Steel Alloy Systems in the 13-volume series Comprehensive Materials Processing 2nd edition by Elsevier; and Quality Control and Quality Assurance - Techniques and Applications. 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He received his MS and Ph.D.\nin Electrical Engineering from the Faculty of Electrical Engineering, University of Belgrade, Serbia, in 1999 and 2007, respectively.\nDr. Stanimirović is currently an associate research professor at\nthe 'Vinča” Institute of Nuclear Sciences - National Institute of\nthe Republic of Serbia, University of Belgrade. Over the years, he\nparticipated in several scientific projects funded by the Ministry of Science, Technological Development and Innovations of the Republic of Serbia. Dr. Stanimirović\nis the recipient of the IEEE Transactions on Components & Packaging Technologies\nBest Paper Award. His current research interests include material characterization\nmeasurements, MEMS, and micro\u002Fnanoscale sensors.","institutionString":"“Vinča” Institute of Nuclear Sciences – National Institute of the Republic of Serbia, University of Belgrade,","institution":null}]}]},"openForSubmissionBooks":{"paginationCount":8,"paginationItems":[{"id":"1004288","title":"The Art of Learning With Rewards - Advances and Applications in Reinforcement Learning","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc000007IdFIIA0\u002F0016192_TrikoderCover%20%282024-06-19%2010%3A49%3A50%29.jpg","hash":"5c1e0c832744542f37ad9cdaa8261e73","secondStepPassed":false,"currentStepOfPublishingProcess":2,"submissionDeadline":"December 6th 2024","isOpenForSubmission":true,"isPublished":false,"editors":[{"id":"236741","title":"Dr.","name":"Tingting","surname":"Zhao","slug":"tingting-zhao","fullName":"Tingting Zhao"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null},{"id":"1004517","title":"The Science of Recommender Systems - Principles, Practices and Challenges","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc0000091cJyIAI\u002F0016421_TrikoderCover%20%282024-07-30%2009%3A22%3A32%29.jpg","hash":"8fe2de9ff600949b732a45ec6150123c","secondStepPassed":false,"currentStepOfPublishingProcess":2,"submissionDeadline":"December 10th 2024","isOpenForSubmission":true,"isPublished":false,"editors":[{"id":"610982","title":"Associate Prof.","name":"Arwa","surname":"Mashat","slug":"arwa-mashat","fullName":"Arwa Mashat"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null},{"id":"1004479","title":"Multi-agent Systems - From Basic Concepts to Cutting-Edge Technologies","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc0000091cJMIAY\u002F0016383_TrikoderCover%20%282024-07-31%2011%3A59%3A58%29.jpg","hash":"33a9504bcb2cab0120d3d1972653e75e","secondStepPassed":false,"currentStepOfPublishingProcess":2,"submissionDeadline":"December 16th 2024","isOpenForSubmission":true,"isPublished":false,"editors":[{"id":"582378","title":"Dr.","name":"Nohaidda","surname":"Sariff","slug":"nohaidda-sariff","fullName":"Nohaidda Sariff"}],"equalEditorOne":null,"equalEditorTwo":null,"equalEditorThree":null},{"id":"1004571","title":"Artificial Intelligence in Medicine and Surgery - An Exploration of Current Trends, Potential Opportunities, and Evolving Threats, Volume 3","coverURL":"https:\u002F\u002Fintech-files.s3.amazonaws.com\u002Fa04Tc000009jOE7IAM\u002F0016475_TrikoderCover%20%282024-08-21%2013%3A18%3A28%29.jpg","hash":"7494a86b547d7bae38a505e112e43647","secondStepPassed":false,"currentStepOfPublishingProcess":2,"submissionDeadline":"December 17th 2024","isOpenForSubmission":true,"isPublished":false,"editors":[{"id":"181694","title":"Dr.","name":"Stanislaw P.","surname":"Stawicki","slug":"stanislaw-p.-stawicki","fullName":"Stanislaw P. 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Prior to his current role, he served as Deputy Director in the Department of Obstetrics and Gynecology at both the Second Clinical College and the Second Affiliated Hospital of Wenzhou Medical University. Dr. Ge possesses 22 years of experience in reproductive medicine, specializing in the clinical application of Assisted Reproductive Technologies (ART) and the comprehensive management of female infertility. He has successfully managed over 10,000 ART cycles, including conventional IVF\u002FICSI treatments, IVM, and oocyte cryopreservation. Dr. Ge's research concentrates on the pathophysiology of polycystic ovary syndrome (PCOS), premature ovarian insufficiency (POI), and the role of mitochondrial function in gamete and embryonic development. He has published over 80 peer-reviewed articles and has been a contributor to a scholarly monograph, thereby contributing significantly to the field's knowledge base and clinical practices in reproductive health.","institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"576122","title":"Dr.","name":"Rong","middleName":null,"surname":"Ju","slug":"rong-ju","fullName":"Rong Ju","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F576122\u002F1712665194\u002Fprofile\u002Fimage1.jpg","biography":"Dr. Ju is a chief physician and deputy dean at the Affiliated Jiangning Hospital of Nanjing Medical University. She received her Ph.D. degree of Obstetrics and Gynecology at Nanjing Medical University in 2016. Dr. Ju serves as a member of the Endocrinology Group of the Obstetrics and Gynecology Branch of Jiangsu Medical Association, a member of the Reproductive Medicine Committee of Jiangsu Medical Association, and the deputy chairman of the Reproductive Medicine branch of the Jiangsu Maternal and Child Health Association. She specializes in gynecological endocrine diseases, endometriosis, female infertility, and assisted pregnancy, as well as geriatric gynecology. She was in charge of mainly participating in 10 scientific projects, published more than 20 papers, and obtained two authorized national invention patents.","institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"178661","title":"Dr.","name":"Wei","middleName":null,"surname":"Wu","slug":"wei-wu","fullName":"Wei Wu","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F178661\u002F1732030632\u002Fprofile\u002Fimage1.jpg","biography":"Dr. Wei Wu serves as Deputy Dean of the School of International Education, Deputy Director of the Department of International Cooperation and Exchange, Professor of the Department of Toxicology at Nanjing Medical University, China. He was a guest researcher at the National Institute of Environmental Health Sciences (NIEHS) between 2017 and 2018. He is the PI of the State Key Laboratory of Reproductive Medicine and Offspring Health, and the Key Laboratory of Modern Toxicology of the Ministry of Education.\n\nHe is a member of different national and international societies in the fields of human reproduction and toxicology, and has received awards from many national societies for the originality and quality of his projects. He has a wide range of teaching and consulting experience, including in toxicology. His research interests include the application of new media technology in teaching, epigenetic mechanisms of transgenerational effects of male infertility induced by endocrine disrupting chemicals, environmental exposure and male reproductive health, genetic and epigenetic risk factors of male infertility and abnormal fetal growth.\n\nProf. Wu has published 100+ papers in peer-reviewed academic journals including Environmental Pollution, EBioMedicine, Environment International, Environmental Health, Clinical Epigenetics, Toxicological Sciences, Human Reproduction, and Molecular Human Reproduction. The H-index is 29. He has edited nine books and collaborated on ten books, 19 patents, and in the organization of three international conferences. Prof. Wu serves as the Editor-in-Chief of international scientific journals International Journal of Sexual Health and Reproductive Health Care, Research International Journal of Endocrinology and Diabetes, Executive Editor of Annals of Molecular and Genetic Medicine, Associate Editor of the JSM Invitro Fertilization, and editor of many other journals including Scientific Reports and Experimental and Therapeutic Medicine.","institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"108807","title":"Ph.D.","name":"Bin","middleName":null,"surname":"Wu","slug":"bin-wu","fullName":"Bin Wu","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F108807\u002F1717205404\u002Fprofile\u002Fimage1.jpg","biography":"Bin Wu, Ph.D., HCLD (ABB) is currently a scientific laboratory director at Arizona Center for Reproductive Endocrinology and Infertility, USA. He received his training in genetics and reproductive biology at the NWAU in China and at Cornell University, as well as post-doctorate training at the University of Guelph, Canada. As an embryologist, he joined the Center for Human Reproduction in Chicago. He has memberships in the American Society for Reproductive Medicine and the American Association of Bioanalysts. Also, he has obtained some significant research awards from professional associations. The American College of Embryology recognized Dr. Wu’s excellence in the practice of reproductive embryology in July 2014. Dr. Wu has published 50 papers and edited five published books in the field of embryology.","institutionString":"Arizona Center for Reproductive Endocrinology and Infertility","institution":null},{"id":"317103","title":"Prof.","name":"Nikolaos","middleName":null,"surname":"Nikolettos","slug":"nikolaos-nikolettos","fullName":"Nikolaos Nikolettos","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F317103\u002F1726041378\u002Fprofile\u002Fimage1.png","biography":"Professor Nikolettos Nikos is a specialist in Obstetrics and Gynecology—Assisted Reproduction at Democritus University of Thrace. He has been trained in gynecological endocrinology, human reproduction, and in vitro fertilization. From 2007 to 2011, he acted as Director of the In Vitro Fertilization Unit of the University Regional General Hospital of Alexandroupolis. From 2012 to 2018, he was Director of the Laboratory of Reproductive Physiology—Artificial Fertilization. In 2018, he became Professor of Obstetrics and Gynecology—Assisted Reproduction. In 2019, he took over the management of the University Obstetrics and Gynecology Clinic at the Medical Department of the Democritus University of Thrace. His scientific work includes more than 100 publications in international journals and many invited lectures at international and Greek conferences.","institutionString":"Democritus University of Thrace","institution":{"name":"Democritus University of Thrace","country":{"name":"Greece"}}},{"id":"522594","title":"Dr.","name":"Alfred A.","middleName":null,"surname":"Shihata","slug":"alfred-a.-shihata","fullName":"Alfred A. Shihata","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F522594\u002F1715145350\u002Fprofile\u002Fimage1.jpg","biography":"Dr. Alfred Shihata is President\u002FCEO of FemCap Inc. as well as the inventor of the Double Balloon Catheter, Shihata percutaneous knife, FemmyCycle™ menstrual cup and FemCap™ cervical cap. He developed many urological and Gynecological procedures. He has six U.S patents and several international patents. He brings more than three decades of research in women’s reproductive health, mainly the prevention of stress urinary incontinence. He used his FemCap to deliver microbicides to prevent the HIV transmission from the male to the Female. He received numerous awards. as a medical device designer.","institutionString":"Scripps Institute of Medicine and science","institution":null},{"id":"48837","title":"Prof.","name":"Panagiotis","middleName":null,"surname":"Tsikouras","slug":"panagiotis-tsikouras","fullName":"Panagiotis Tsikouras","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F48837\u002F1726041371\u002Fprofile\u002Fimage1.jpg","biography":"Panagiotis Tsikouras is a specialist in obstetrics and gynecology, perinatal medicine, and contraception at the School of Medicine, Democritus University of Thrace, Greece. He is also head of the Family Planning Centre and Gynecological Cytology Laboratory at the same university. Dr. Tsikouras is a fellow of the International Academy of Clinical and Applied Thrombosis\u002FHemostasis. His scientific activities focus on pediatric and adolescent medicine, gynecological oncology, and high-risk pregnancies. He is a reviewer for several international journals and has numerous scientific publications to his credit, including papers and book chapters. He has also contributed to international and national guidelines on coagulation and thrombosis in obstetrics and gynecology.","institutionString":"Democritus University of Thrace","institution":{"name":"Democritus University of Thrace","country":{"name":"Greece"}}},{"id":"287503","title":"Dr.","name":"Kristina","middleName":null,"surname":"Roloff","slug":"kristina-roloff","fullName":"Kristina Roloff","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F287503\u002F1715148696\u002Fprofile\u002Fimage1.jpg","biography":"Dr. Kristina (Kristy) Roloff is a Maternal Medicine (MFM) attending at Arrowhead Regional Medical Center (ARMC) in Colton, CA. She received her degree in Osteopathic Medicine from Western University of Health Sciences in 2006, and completed residency in Obstetrics and Gynecology in 2010. She practiced as a full time attending at ARMC while assisting with curriculum development and the approval process for the MFM Fellowship, and graduated as the first fellow through the program in July 2015. She also obtained a Master’s in public health with an emphasis in community health science from UCLA. She is now the Program Director for the MFM Fellowship program at ARMC.\r\nBefore medical school, Dr. Roloff was interested in space exploration. Her undergraduate degree from McGill University, Montreal, Quebec, is in Earth and Planetary Science. She earned a Masters Degree in Astronomy from the University of British Columbia, Vancouver, BC, where she was a member of the team that launched MOST, Canada's first microsatellite. The satellite is now collecting space dust, but collected data and performed its intended science for 11 years.\r\nDr. Roloff maintains a curious nature – but these days focuses on research that may improve the maternal health of the patients in her community. Her current research activities include study of methods to improve elective induction of labor and patient experiences and health care disparities.","institutionString":"Arrowhead Regional Medical Center, United States of America","institution":{"name":"Arrowhead Regional Medical Center","country":{"name":"United States of America"}}},{"id":"438131","title":"Prof.","name":"Anna Maria","middleName":null,"surname":"Paoletti","slug":"anna-maria-paoletti","fullName":"Anna Maria Paoletti","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F438131\u002F1716290571\u002Fprofile\u002Fimage1.png","biography":"PERSONAL INFORMATION\tPaoletti Anna Maria \n\n\t office. cellular phone 3391947282 \n\n\t gineca.annapaoletti@tiscali.it\ngineca.annapaoletti@gmail.com\nannamaria.paoletti@ca.omceo.it \n \n\tDate of birth SEPTEMBER 18, 1950 Fiscal Code PLTNMR50P58B354I\n\nPROFESSIONAL EXPERIENCE\t \n\n\tHead of the Head of the Department of Obstetrics and Gynecology of the Azienda Ospedaliero Universitaria di Cagliari and Head of the Department Materno Infantile (Azienda Ospedaliero Universitaria di Cagliari)\nSince 2018 up to 30 september 2020\n\nHead of the Department Materno Infantile (Azienda Ospedaliero Universitaria di Cagliari)\nSince 2018 up to 30 september 2020\n\nFull professor of Gynecology and Obstetrics\n\tUNIVERSITY OF CAGLIARI, ITALY\n2006 up to 30 september 2020\n\n\tDirector of the School of Specialization in Obstetrics and Gynecology, Faculty of Medicine, University of Cagliari, Italy\nSince 2003 to 2018\n\n\tResponsible - U.O.C. Obstetrics and Gynecology\nUniversity of Cagliari\nFrom 2010 to June 2011\n\n\tAssociate Professor of Obstetrics and Gynecology, Faculty of Medicine and Surgery\nUNIVERSITY 'CAGLIARI\nFrom 2000 to 2006\n\t\n\n\tProfessor in Obstetrics and Gynecology\nUNIVERSITY 'CAGLIARI\nFrom 1993 to 2000\n\t\n\n\tProfessor in Obstetrics and Gynecology\nUNIVERSITY OF PISA\nFrom 1980 to 1993\n\n\tFellow Department of Education, Department of Obstetrics and Gynecology\nUNIVERSITY 'OF PISA\nFrom 1976 to 1980\n\n\tFellow Ministry of Education, Institute of Obstetrics and Gynaecology\nUNIVERSITY 'CAGLIARI\nFrom 1976 to 1980\n\t\n\nEDUCATION AND TRAINING\t \n\nSpecialist in Andrology\n\nSpecialist in Gynecology and Obstetrics\n\nDegree in medicine and surgery\n \nPERSONAL SKILLS\t \n\n\t\nOther language\tUNDERSTANDING\tSPEAKING\tWRITING\n\tListening\tReading\tInteraction\tOral production\t\nEnglish\tA2\tA2\tA2\tA2\tB1\n\tLevels: A1 and A2: Basic User - B1 and B2: Independent user - C1 and C2: Power Users\nCommon European Framework of Reference for Languages \n\n\nother skills\tIn addition to technology expertise obstetrical and gynecological, documented in clinical and scientific curriculum vitae, is the comprehensive view of the technologies used in teaching and organizational.\n\nMORE INFORMATION\t \n\n\tInternational opinion leaders in the fields of Gynecologic Endocrinology, Contraception, Menopause, Fertility and Sterility.\nAuthor of over 650 scientific publications (211 international journals with high impact factor, see Scopus) as well as monographs, book chapters and manuals of obstetrics and gynecology. And scientific director of numerous clinical trials.\n• Scopus Documents:211 Analyze author output :\n• Citations: 4,277 citations by 3,601 documents\n• h-index: 36\n \n\n\tMember of the organizing committee of more than 110 courses updates, seminars, national and international conferences Scientific Research Projects and Health Education, funded by the University, the Ministry and the Region of Sardinia. Scientific director of numerous experimental research protocols at national and international level, some of which took place as the National Coordinator. \nMember of the Management Committee of \nthe Italian Society of Gynecology and Obstetrics from 2017 up to 2019, member the Management Committee of \n•\tthe Italian Society of Menopause, \n•\tthe Italian Society of Contraception, \n•\tthe Italian Association of Gynecological Endocrinology (Associazione Italiana Ginecologia Endocrinologica, AIGE)\n•\tthe Working Group on Menopause and Gynecological Endocrinology promoted by SIGO (Società Italiana di Ginecologia e Ostetricia).\n\n\n 2010 - 2014 Expert Clinical Ethics Committee of the University Hospital of Cagliari.\n\t \nPersonal data\t\tI authorize the use of my personal data pursuant to Legislative Decree 30 June 2003 n. 196 \"Code concerning the protection of personal data.\n\nDate and signature\t\nMAY 18, 2024\nAnna Maria Paoletti","institutionString":null,"institution":{"name":"University of Cagliari","country":{"name":"Italy"}}},{"id":"173834","title":"Prof.","name":"Georgios","middleName":null,"surname":"Androutsopoulos","slug":"georgios-androutsopoulos","fullName":"Georgios Androutsopoulos","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F173834\u002F1732005242\u002Fprofile\u002Fimage1.jpg","biography":"Georgios Androutsopoulos completed his Degree in Medicine at the National and Kapodestrian University of Athens, in 1995. Prof. Androutsopoulos received his Medical Specialization at the Department of Obstetrics - Gynaecology of the University of Patras, in 2006. He also completed his Doctorate in Medicine at the same Department, in 2007.\nHe started his academic career as a Lecturer and Consultant at the Department of Obstetrics - Gynecology of the University of Patras School of Medicine in 2012. Currently, he is an associate professor, consultant, and head of the gynaecological oncology unit in the same department.\nHis research interests are mainly focused on Obstetrics - Gynaecology and Gynaecological Oncology. He has authored 7 Chapters in Scientific Books and 45 articles in International Scientific Journals.","institutionString":"School of Medicine, University of Patras","institution":null},{"id":"543358","title":"Dr.","name":"Maria Fernanda","middleName":null,"surname":"Calderon Leon","slug":"maria-fernanda-calderon-leon","fullName":"Maria Fernanda Calderon Leon","position":null,"cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F543358\u002F1722276753\u002Fprofile\u002Fimage1.jpg","biography":"medico especialista en Ginecologia y Obstetricia, estudios de postgrado realizados en Universidad de Guayaquil, estudios de pregrado realizados en universidad catolica de Santiago de Guayaquil.","institutionString":"Hospital Universitario de Guayaquil","institution":null},{"id":"592578","title":"Dr.","name":"Ana Maria","middleName":null,"surname":"Apetrei","slug":"ana-maria-apetrei","fullName":"Ana Maria Apetrei","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Elena Doamna Maternity, Iași","institution":null},{"id":"592570","title":"Assistant Prof.","name":"Ana Maria","middleName":null,"surname":"Haliciu","slug":"ana-maria-haliciu","fullName":"Ana Maria Haliciu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Gr. T. Popa University of Medicine and Pharmacy, Iași","institution":null},{"id":"600627","title":"Prof.","name":"German William","middleName":null,"surname":"Rangel","slug":"german-william-rangel","fullName":"German William Rangel","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Universidad Autonoma de Bucaramanga (Colombia)","institution":null},{"id":"309358","title":"Dr.","name":"Ioana","middleName":null,"surname":"Pavaleanu","slug":"ioana-pavaleanu","fullName":"Ioana Pavaleanu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Grigore T. Popa University of Medicine and Pharmacy","country":{"name":"Romania"}}},{"id":"88787","title":"Dr.","name":"Razvan","middleName":null,"surname":"Socolov","slug":"razvan-socolov","fullName":"Razvan Socolov","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":"Razvan Socolov currently works at the Department of Obstetrics and Gynecology, Universitatea de Medicina si Farmacie Grigore T. Popa Iasi. Razvan does research in Gynaecology, Surgery and Obstetrics. The most recent publication is 'Early Diagnosis and Treatment of Dental Caries in Pregnancy'. Particular research interest fields are reproductive surgery, endometriosis, gynecologic endoscopy.","institutionString":null,"institution":{"name":"Grigore T. Popa University of Medicine and Pharmacy","country":{"name":"Romania"}}},{"id":"600626","title":"Prof.","name":"Sudhir","middleName":null,"surname":"Diwan","slug":"sudhir-diwan","fullName":"Sudhir Diwan","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Advanced Spine on Park Avenue, NY, USA","institution":null},{"id":"611269","title":"Assistant Prof.","name":"Teodora","middleName":null,"surname":"Balan","slug":"teodora-balan","fullName":"Teodora Balan","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Gr T Popa University of Medicine and Pharmacy, Iași, Romania","institution":null},{"id":"592569","title":"Dr.","name":"Tiberiu Nicolae","middleName":null,"surname":"Poparlan","slug":"tiberiu-nicolae-poparlan","fullName":"Tiberiu Nicolae Poparlan","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Elena Doamna Maternity, Iași","institution":null},{"id":"592577","title":"Assistant Prof.","name":"Tudor Andrei","middleName":null,"surname":"Butureanu","slug":"tudor-andrei-butureanu","fullName":"Tudor Andrei Butureanu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Gr. T. Popa University of Medicine and Pharmacy, Iași","institution":null},{"id":"611878","title":"M.Sc.","name":"Balansama","middleName":null,"surname":"Marah","slug":"balansama-marah","fullName":"Balansama Marah","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611874","title":"B.Sc.","name":"Feng","middleName":null,"surname":"Wu","slug":"feng-wu","fullName":"Feng Wu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611875","title":"B.Sc.","name":"Haonan","middleName":null,"surname":"Shi","slug":"haonan-shi","fullName":"Haonan Shi","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611883","title":"M.D.","name":"Jing","middleName":null,"surname":"Wei","slug":"jing-wei","fullName":"Jing Wei","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"The Affiliated Taizhou People’s Hospital to Nanjing Medical University","institution":null},{"id":"611881","title":"B.Sc.","name":"Lei","middleName":null,"surname":"Chen","slug":"lei-chen","fullName":"Lei Chen","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611415","title":"B.Sc.","name":"Peihao","middleName":null,"surname":"Wu","slug":"peihao-wu","fullName":"Peihao Wu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611885","title":"M.Sc.","name":"Qi","middleName":null,"surname":"Liu","slug":"qi-liu","fullName":"Qi Liu","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611414","title":"B.Sc.","name":"Qinrou","middleName":null,"surname":"Chen","slug":"qinrou-chen","fullName":"Qinrou Chen","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611879","title":"M.Sc.","name":"Sia Florence","middleName":null,"surname":"Koroma","slug":"sia-florence-koroma","fullName":"Sia Florence Koroma","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":null,"institution":{"name":"Nanjing Medical University","country":{"name":"China"}}},{"id":"611873","title":"B.Sc.","name":"Tongfei","middleName":null,"surname":"Yang","slug":"tongfei-yang","fullName":"Tongfei Yang","position":null,"cdnProfilePictureURL":"\u002F\u002Fcdnintech.com\u002Fweb\u002Ffrontend\u002Fwww\u002Fassets\u002F45.123\u002Fauthor.svg","biography":null,"institutionString":"Nanjing Medical University","institution":null}]}},"subseries":{"item":{"id":"97","type":"subseries","title":"Nanomaterials and Nanostructures","keywords":"Nanoparticle, Nanotube, Nanofiber, Nanorod, Metals, Dendrimers, Smart Nanomaterials, Electrical Properties, Mechanical Properties, Magnetic Properties, Thermal Properties, Drug Delivery, Health Treatments, Supercapacitors, Catalysts, Sensors, Top-down Manufacturing, Bottom-up Manufacturing, Carbon Nanostructures, Magnetic Nanoparticles, Functionalization, Thermal Interface Materials, Coatings, Adhesives","scope":"\u003Cp\u003E\r\n\tThe interest in developing new nanomaterials has been growing over the last decades with multiple new advances in manufacturing, modifying, characterizing, and, more recently, applying nanomaterials and nanostructures at both scientific and industrial levels. Nanomaterials and Nanostructures topic examines nanomaterials of different dimensions (0-D, 1-D, and 2-D) without limitation in terms of geometry or morphology to give a broad overview of their potential use and current challenges. The scope of this topic includes nanomaterials and nanostructures of different natures, such as metallic, ceramic, and polymeric ones, but also any other combination of these to create nanocomposites and other inorganic approximations that do not fit properly in the previously categorized origins. For each of the main nanomaterial families, three different aspects or levels will be dealt with: synthesis or manufacturing, characterization, and application in different technological areas such as transportation technologies, energy production and storage, health, and electronic and communications technology.\u003C\u002Fp\u003E","coverUrl":"https:\u002F\u002Fcdn.intechopen.com\u002Fseries_topics\u002Fcovers\u002F97.jpg","hasOnlineFirst":true,"hasPublishedBooks":true,"annualVolume":13469,"isSalesforceSubseries":false,"editor":{"id":"320054","title":"Dr.","name":"Alberto","middleName":null,"surname":"Jiménez-Suárez","slug":"alberto-jimenez-suarez","fullName":"Alberto Jiménez-Suárez","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F320054\u002F1703170808\u002Fprofile\u002Fimage1.jpg","biography":"Alberto Jiménez-Suárez is a senior lecturer at Universidad Rey Juan Carlos in the Materials Science and Engineering Area. Started almost 15 years ago his research is in the field of the incorporation of nanoparticles to polymer matrices to confer them new functionalities. His initial research was mainly focused on the obtention of electrically conductive epoxy-based nanocomposites with particular attention on the manufacturing parameters that may affect their dispersion in the polymer matrices. Later, the research was applied to the development of new functionalities such as structural health monitoring, self-heating for de-and anti-icing systems, or thermal activation of polymers with self-healing and self-heating capabilities. Finally, current research continues with the development of new nanocomposites and multiscale reinforced composites, but also with a perspective of their environmental impact. He is the author of more than 80 JCR-indexed articles with an h-index of 22 according to the Scopus database. Currently, he is sub-director of the Official Master School at Universidad Rey Juan Carlos, in charge of End-of-Master Projects, External Internships, and Companies Relations.","institutionString":"King Juan Carlos University, Spain","institution":{"name":"King Juan Carlos University","institutionURL":null,"country":{"name":"Spain"}}},"editorTwo":{"id":"567726","title":"Dr.","name":"Gonzalo","middleName":null,"surname":"Seisdedos","slug":"gonzalo-seisdedos","fullName":"Gonzalo Seisdedos","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F567726\u002F1703170810\u002Fprofile\u002Fimage1.jpg","biography":"Gonzalo Seisdedos Rodriguez is a postdoc research associate at Los Alamos National Laboratory in the Materials Synthesis and Applications group. Gonzalo obtained his bachelor’s degree in mechanical engineering at Florida International University (Miami, USA), where he also obtained his master’s degree and Ph.D. in materials science and engineering. At the beginning of his graduate studies, he focused his research on the effect of substrate contamination in adhesive bonds of reinforced carbon fiber composites for aerospace applications. He then continued with the non-destructive evaluation of the curing process of epoxy adhesives using magneto-electric nanoparticles. He now focuses his research on the in-situ, non-destructive evaluation of polymeric materials using ultrasonics to investigate how the manufacturing parameters affect the cure kinetics and final properties of the polymers. This novel evaluation method can help optimize the design and tailoring process of polymers and can also be used during manufacturing for quality control, which will help reduce plastic waste in an R&D and manufacturing setting.","institutionString":null,"institution":{"name":"Los Alamos National Laboratory","institutionURL":null,"country":{"name":"United States of America"}}},"editorThree":null,"associateEditorOne":null,"associateEditorTwo":null,"associateEditorThree":null,"series":{"id":"26","title":"Nanotechnology and Nanomaterials","doi":"10.5772\u002Fintechopen.107191","issn":"3029-0538"},"editorialBoard":[{"id":"198180","title":"Dr.","name":"Maddalena","middleName":null,"surname":"Pedio","slug":"maddalena-pedio","fullName":"Maddalena Pedio","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F198180\u002F1679474634\u002Fprofile\u002Fimage1.jpg","institutionString":null,"institution":{"name":"National Research Council","institutionURL":null,"country":{"name":"Italy"}}},{"id":"278962","title":"Dr.","name":"Mostapha","middleName":null,"surname":"Tarfaoui","slug":"mostapha-tarfaoui","fullName":"Mostapha Tarfaoui","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F278962\u002F1684935438\u002Fprofile\u002Fimage1.jpg","institutionString":"ENSTA Bretagne IRDL UMR CNRS 6027, Brest, France","institution":null},{"id":"163154","title":"Dr.","name":"Sergio Alfonso","middleName":null,"surname":"Pérez García","slug":"sergio-alfonso-perez-garcia","fullName":"Sergio Alfonso Pérez García","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F163154\u002F1702548508\u002Fprofile\u002Fimage1.jpg","institutionString":null,"institution":{"name":"Centro de Investigación en Materiales Avanzados","institutionURL":null,"country":{"name":"Mexico"}}}],"_topicEditors":[{"id":"320054","title":"Dr.","name":"Alberto","middleName":null,"surname":"Jiménez-Suárez","slug":"alberto-jimenez-suarez","fullName":"Alberto Jiménez-Suárez","cdnProfilePictureURL":"https:\u002F\u002Fcdnintech.com\u002Fmedia\u002Fauthor\u002F320054\u002F1703170808\u002Fprofile\u002Fimage1.jpg","biography":"Alberto Jiménez-Suárez is a senior lecturer at Universidad Rey Juan Carlos in the Materials Science and Engineering Area. Started almost 15 years ago his research is in the field of the incorporation of nanoparticles to polymer matrices to confer them new functionalities. His initial research was mainly focused on the obtention of electrically conductive epoxy-based nanocomposites with particular attention on the manufacturing parameters that may affect their dispersion in the polymer matrices. Later, the research was applied to the development of new functionalities such as structural health monitoring, self-heating for de-and anti-icing systems, or thermal activation of polymers with self-healing and self-heating capabilities. Finally, current research continues with the development of new nanocomposites and multiscale reinforced composites, but also with a perspective of their environmental impact. He is the author of more than 80 JCR-indexed articles with an h-index of 22 according to the Scopus database. 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