Bayesian Experimental Design - Mathematical Sciences Home Pages
Bayesian Experimental Design - Mathematical Sciences Home Pages
Bayesian Experimental Design - Mathematical Sciences Home Pages
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6.7<strong>Design</strong>problemsinreliabilityandqualitycontrol ponentiallifetimeswhereexperimentalunitsmay,ormaynot,besubjecttoanincreased stressandwhereunitsmaybesubjecttoahighstress,iftheydonotfailinaspecied periodoftimeunderalowstress.DeGrootandGoelcallthis\tampering".Theyderived exact<strong>Bayesian</strong>optimaldesignsunderparticularlossfunctionsandcosts.DeGrootandGoel DeGrootandGoel(1979)considereda<strong>Bayesian</strong>approachtodesigningstudiesofex(1988)isareviewofthisworkandappearedinavolume,ClarottiandLindley(1988),deoptimaldesignsforacceleratedlifetestingwherethelifetimeshaveeitherWeibullorlog-<br />
diagramsandtheiruseinoptimaldesign. papers:forexamplethechapterbyBarlow,MensingandSmiriga(1988)discussesinuence votedto<strong>Bayesian</strong>analysisanddesigninreliability.Thisvolumealsocontainsotherrelevantnormaldistributionsandthelengthoftimeavailablefortheexperimentisxed.TheirmethodsareextendedinNaylor(1994).Verdinelli,PolsonandSingpurwalla(1993)discussed<strong>Bayesian</strong>designforacceleratedlifetestingexperimentswherepredictionisthegoal.<br />
ChalonerandLarntz(1992)tooktheapproachdescribedinSection4.2toderive<strong>Bayesian</strong><br />
informationinagrouptestingexperiment:theyprovidedfreesoftwarefortheirmethod. havealognormaldistribution.MitchellandScott(1987)alsodesignedtomaximizeShannon TheyusedShannoninformationin(9)asutilityandconsideredthecasewherethelifetimes<br />
valueandtominimizethepredictivevariance. targetwhichisanimportantproblemintheTaguchiapproachtodesign.Theyproposed, 6.8Largecomputerexperiments asa<strong>Bayesian</strong>alternativetonon-<strong>Bayesian</strong>methods,tosetthepredictivemeanatthetarget VerdinelliandWynn(1988)examinedsomeaspectsofkeepinganexpectedresponseon<br />
Thesituationcanbethoughtofashavingaresponsesurfacewhichisknowntobesmooth butitsgeneralformisunknownandthevaluesoftheresponsesurfacecanbedetermined totheproblemofchoosingthevaluesatwhichtorunalargedeterministiccomputermodel. withouterror.Sacks,Welch,MitchellandWynn(1989)reviewthiswork.Recentadvances Someexcitingrecentdevelopmentshaveoccurredinapplyingideasfromoptimaldesign<br />
aredescribedinWelchetal(1992),Morris,MitchellandYlvisaker(1993)andBates,Buck, 46
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