Bayesian Methods for Planning Accelerated Life Tests
This article describes Bayesian methods for accelerated life test planning with one accelerating variable, when the acceleration model is linear in the parameters, based on censored data from a log-location-scale distribution. We use a Bayesian criterion based on estimation precision of a distributi...
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| Veröffentlicht in: | Technometrics 2006-02, Vol.48 (1), p.49-60 |
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| container_title | Technometrics |
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| creator | Zhang, Yao Meeker, William Q |
| description | This article describes Bayesian methods for accelerated life test planning with one accelerating variable, when the acceleration model is linear in the parameters, based on censored data from a log-location-scale distribution. We use a Bayesian criterion based on estimation precision of a distribution quantile at a specified use condition to find optimum test plans. We also show how to compute optimized compromise plans that satisfy practical constraints. A large-sample normal approximation provides an easy-to-interpret yet useful simplification to this planning problem. We present a numerical example using the Weibull distribution with type I censoring to illustrate the methods and to examine the effects of the prior distribution, censoring, and sample size. The general equivalence theorem is used to verify that the numerically optimized test plans are globally optimum. The resulting optimum plans are also evaluated using simulation. |
| doi_str_mv | 10.1198/004017005000000373 |
| format | Article |
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We use a Bayesian criterion based on estimation precision of a distribution quantile at a specified use condition to find optimum test plans. We also show how to compute optimized compromise plans that satisfy practical constraints. A large-sample normal approximation provides an easy-to-interpret yet useful simplification to this planning problem. We present a numerical example using the Weibull distribution with type I censoring to illustrate the methods and to examine the effects of the prior distribution, censoring, and sample size. The general equivalence theorem is used to verify that the numerically optimized test plans are globally optimum. The resulting optimum plans are also evaluated using simulation.</description><identifier>ISSN: 0040-1706</identifier><identifier>EISSN: 1537-2723</identifier><identifier>DOI: 10.1198/004017005000000373</identifier><identifier>CODEN: TCMTA2</identifier><language>eng</language><publisher>Alexandria, VI: Taylor & Francis</publisher><subject>Accelerated life tests ; Activation energy ; Applied sciences ; Approximation ; Bayesian analysis ; c-optimality ; Censored data ; Censorship ; Computer science; control theory; systems ; Data processing. List processing. Character string processing ; Distribution planning ; Equivalence theorem ; Estimating techniques ; Exact sciences and technology ; Inference ; Log-location-scale family ; Mathematics ; Memory organisation. Data processing ; Modeling ; Optimal design ; Parametric models ; Planning ; Preposterior ; Probability and statistics ; Reliability ; Sample size ; Sciences and techniques of general use ; Simulations ; Software ; Statistical variance ; Statistics</subject><ispartof>Technometrics, 2006-02, Vol.48 (1), p.49-60</ispartof><rights>American Statistical Association and the American Society for Quality 2006</rights><rights>Copyright 2006 The American Statistical Association and The American Society for Quality</rights><rights>2006 INIST-CNRS</rights><rights>Copyright American Society for Quality Feb 2006</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-2c09257a7f54a0f7e2619250b4d6bad18b1f8a8951fa3946f6d16a6d279bcf2e3</citedby><cites>FETCH-LOGICAL-c380t-2c09257a7f54a0f7e2619250b4d6bad18b1f8a8951fa3946f6d16a6d279bcf2e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/25471114$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/25471114$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17473517$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Zhang, Yao</creatorcontrib><creatorcontrib>Meeker, William Q</creatorcontrib><title>Bayesian Methods for Planning Accelerated Life Tests</title><title>Technometrics</title><description>This article describes Bayesian methods for accelerated life test planning with one accelerating variable, when the acceleration model is linear in the parameters, based on censored data from a log-location-scale distribution. We use a Bayesian criterion based on estimation precision of a distribution quantile at a specified use condition to find optimum test plans. We also show how to compute optimized compromise plans that satisfy practical constraints. A large-sample normal approximation provides an easy-to-interpret yet useful simplification to this planning problem. We present a numerical example using the Weibull distribution with type I censoring to illustrate the methods and to examine the effects of the prior distribution, censoring, and sample size. The general equivalence theorem is used to verify that the numerically optimized test plans are globally optimum. The resulting optimum plans are also evaluated using simulation.</description><subject>Accelerated life tests</subject><subject>Activation energy</subject><subject>Applied sciences</subject><subject>Approximation</subject><subject>Bayesian analysis</subject><subject>c-optimality</subject><subject>Censored data</subject><subject>Censorship</subject><subject>Computer science; control theory; systems</subject><subject>Data processing. List processing. Character string processing</subject><subject>Distribution planning</subject><subject>Equivalence theorem</subject><subject>Estimating techniques</subject><subject>Exact sciences and technology</subject><subject>Inference</subject><subject>Log-location-scale family</subject><subject>Mathematics</subject><subject>Memory organisation. Data processing</subject><subject>Modeling</subject><subject>Optimal design</subject><subject>Parametric models</subject><subject>Planning</subject><subject>Preposterior</subject><subject>Probability and statistics</subject><subject>Reliability</subject><subject>Sample size</subject><subject>Sciences and techniques of general use</subject><subject>Simulations</subject><subject>Software</subject><subject>Statistical variance</subject><subject>Statistics</subject><issn>0040-1706</issn><issn>1537-2723</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1Lw0AQhhdRsFb_gCAEwWN0Zz-TgwctfkFFD_UcJsmupqTZupsi_fduTdWD4FwG5n3mneEl5BjoOUCeXVAqKGhKJf0qrvkOGYHkOmWa8V0y2gBpJNQ-OQhhTilwlukREde4NqHBLnk0_ZurQ2KdT55b7Lqme02uqsq0xmNv6mTaWJPMTOjDIdmz2AZztO1j8nJ7M5vcp9Onu4fJ1TSteEb7lFU0Z1KjtlIgtdowBXFAS1GrEmvISrAZZrkEizwXyqoaFKqa6bysLDN8TE4H36V376t4uZi7le_iyYIBVxqElBFiA1R5F4I3tlj6ZoF-XQAtNuEUf8OJS2dbZwwVttZjVzXhd1MLzSXoyJ0M3Dz0zv_oTAoNACLql4PedDG3BX4439ZFj-vW-W9T_s8fn_pRffs</recordid><startdate>20060201</startdate><enddate>20060201</enddate><creator>Zhang, Yao</creator><creator>Meeker, William Q</creator><general>Taylor & Francis</general><general>The American Society for Quality and The American Statistical Association</general><general>American Society for Quality Control</general><general>American Statistical Association</general><general>American Society for Quality</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8C1</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>FYUFA</scope><scope>F~G</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>K60</scope><scope>K6~</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M2P</scope><scope>M7S</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope><scope>S0X</scope></search><sort><creationdate>20060201</creationdate><title>Bayesian Methods for Planning Accelerated Life Tests</title><author>Zhang, Yao ; Meeker, William Q</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-2c09257a7f54a0f7e2619250b4d6bad18b1f8a8951fa3946f6d16a6d279bcf2e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Accelerated life tests</topic><topic>Activation energy</topic><topic>Applied sciences</topic><topic>Approximation</topic><topic>Bayesian analysis</topic><topic>c-optimality</topic><topic>Censored data</topic><topic>Censorship</topic><topic>Computer science; control theory; systems</topic><topic>Data processing. List processing. Character string processing</topic><topic>Distribution planning</topic><topic>Equivalence theorem</topic><topic>Estimating techniques</topic><topic>Exact sciences and technology</topic><topic>Inference</topic><topic>Log-location-scale family</topic><topic>Mathematics</topic><topic>Memory organisation. Data processing</topic><topic>Modeling</topic><topic>Optimal design</topic><topic>Parametric models</topic><topic>Planning</topic><topic>Preposterior</topic><topic>Probability and statistics</topic><topic>Reliability</topic><topic>Sample size</topic><topic>Sciences and techniques of general use</topic><topic>Simulations</topic><topic>Software</topic><topic>Statistical variance</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Yao</creatorcontrib><creatorcontrib>Meeker, William Q</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Public Health Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>Health Research Premium Collection</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ABI/INFORM Global</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><collection>SIRS Editorial</collection><jtitle>Technometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Yao</au><au>Meeker, William Q</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bayesian Methods for Planning Accelerated Life Tests</atitle><jtitle>Technometrics</jtitle><date>2006-02-01</date><risdate>2006</risdate><volume>48</volume><issue>1</issue><spage>49</spage><epage>60</epage><pages>49-60</pages><issn>0040-1706</issn><eissn>1537-2723</eissn><coden>TCMTA2</coden><abstract>This article describes Bayesian methods for accelerated life test planning with one accelerating variable, when the acceleration model is linear in the parameters, based on censored data from a log-location-scale distribution. We use a Bayesian criterion based on estimation precision of a distribution quantile at a specified use condition to find optimum test plans. We also show how to compute optimized compromise plans that satisfy practical constraints. A large-sample normal approximation provides an easy-to-interpret yet useful simplification to this planning problem. We present a numerical example using the Weibull distribution with type I censoring to illustrate the methods and to examine the effects of the prior distribution, censoring, and sample size. The general equivalence theorem is used to verify that the numerically optimized test plans are globally optimum. The resulting optimum plans are also evaluated using simulation.</abstract><cop>Alexandria, VI</cop><cop>Milwaukee, WI</cop><pub>Taylor & Francis</pub><doi>10.1198/004017005000000373</doi><tpages>12</tpages></addata></record> |
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| ispartof | Technometrics, 2006-02, Vol.48 (1), p.49-60 |
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| subjects | Accelerated life tests Activation energy Applied sciences Approximation Bayesian analysis c-optimality Censored data Censorship Computer science control theory systems Data processing. List processing. Character string processing Distribution planning Equivalence theorem Estimating techniques Exact sciences and technology Inference Log-location-scale family Mathematics Memory organisation. Data processing Modeling Optimal design Parametric models Planning Preposterior Probability and statistics Reliability Sample size Sciences and techniques of general use Simulations Software Statistical variance Statistics |
| title | Bayesian Methods for Planning Accelerated Life Tests |
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