Table Of Content(cid:2)
AcceleratedLifeTestingofOne-shotDevices
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Accelerated Life Testing of One-shot Devices
Data Collection And Analysis
Narayanaswamy Balakrishnan
McMasterUniversity
Hamilton,Canada
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Man Ho Ling
TheEducationUniversityofHongKong
TaiPo,HongKongSAR,China
Hon Yiu So
UniversityofWaterloo
Waterloo,Canada
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Thisfirsteditionfirstpublished2021
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LibraryofCongressCataloging-in-PublicationData
Names:Balakrishnan,Narayanaswamy.,1956-author.|Ling,ManHo,author.|So,Hon
Yiu,author.
Title:Acceleratedlifetestingofone-shotdevices:datacollectionand
analysis/NarayanaswamyBalakrishnan,McMasterUniversity,Hamilton,
Canada,ManHoLing,TheEducationUniversityofHong,Kong,New
Territories,HongKong,HonYiuSo,UniversityofWaterloo,Waterloo,
Canada.
Description:Firstedition.|Hoboken,NJ,USA:Wiley,2021.|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2020035725(print)|LCCN2020035726(ebook)|ISBN
9781119664000(cloth)|ISBN9781119664017(adobepdf)|ISBN
9781119663942(epub)
Subjects:LCSH:Acceleratedlifetesting.|Failureanalysis(Engineering)
Classification:LCCTA169.3.B352021(print)|LCCTA169.3(ebook)|DDC
620/.00452–dc23
LCrecordavailableathttps://lccn.loc.gov/2020035725
LCebookrecordavailableathttps://lccn.loc.gov/2020035726
CoverDesign:Wiley
CoverImage:©Piergiov/GettyImages
Setin9.5/12.5ptSTIXTwoTextbySPiGlobal,Chennai,India
10 9 8 7 6 5 4 3 2 1
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Withgreatloveandaffection,wededicatethisbookto
SarahandJuliaBalakrishnan,andColleenCutler NB
GraceChu,SophiaLing,andSheldonLing MHL
TianFengandVictoriaSo HYS
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vii
Contents
Preface xi
AbouttheCompanionWebsite xiii
1 One-ShotDeviceTestingData 1
1.1 BriefOverview 1
1.2 One-ShotDevices 1
1.3 AcceleratedLife-Tests 3
1.4 ExamplesinReliabilityandSurvivalStudies 4
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1.4.1 Electro-ExplosiveDevicesData 4
1.4.2 GlassCapacitorsData 5
1.4.3 SolderJointsData 5
1.4.4 Grease-BasedMagnetorheologicalFluidsData 6
1.4.5 MiceTumorToxicologicalData 7
1.4.6 ED01ExperimentData 7
1.4.7 SerialSacrificeData 7
1.5 RecentDevelopmentsinOne-ShotDeviceTestingAnalysis 10
2 LikelihoodInference 13
2.1 BriefOverview 13
2.2 UnderCSALTsandDifferentLifetimeDistributions 13
2.3 EM-Algorithm 14
2.3.1 ExponentialDistribution 16
2.3.2 GammaDistribution 18
2.3.3 WeibullDistribution 21
2.4 IntervalEstimation 26
2.4.1 AsymptoticConfidenceIntervals 26
2.4.2 ApproximateConfidenceIntervals 28
2.5 SimulationStudies 30
2.6 CaseStudieswithRCodes 41
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viii Contents
3 BayesianInference 47
3.1 BriefOverview 47
3.2 BayesianFramework 47
3.3 ChoiceofPriors 49
3.3.1 LaplacePrior 49
3.3.2 NormalPrior 49
3.3.3 BetaPrior 50
3.4 SimulationStudies 51
3.5 CaseStudywithRCodes 59
4 ModelMis-SpecificationAnalysisandModelSelection 65
4.1 BriefOverview 65
4.2 ModelMis-SpecificationAnalysis 65
4.3 ModelSelection 66
4.3.1 AkaikeInformationCriterion 66
4.3.2 BayesianInformationCriterion 67
4.3.3 Distance-BasedTestStatistic 68
4.3.4 ParametricBootstrapProcedureforTestingGoodness-of-Fit 70
4.4 SimulationStudies 70
4.5 CaseStudywithRCodes 76
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5 RobustInference 79
5.1 BriefOverview 79
5.2 WeightedMinimumDensityPowerDivergenceEstimators 79
5.3 AsymptoticDistributions 81
5.4 RobustWald-typeTests 82
5.5 InfluenceFunction 83
5.6 SimulationStudies 85
5.7 CaseStudywithRCodes 91
6 Semi-ParametricModelsandInference 95
6.1 BriefOverview 95
6.2 ProportionalHazardsModels 95
6.3 LikelihoodInference 97
6.4 TestofProportionalHazardRates 99
6.5 SimulationStudies 100
6.6 CaseStudieswithRCodes 102
7 OptimalDesignofTests 105
7.1 BriefOverview 105
7.2 OptimalDesignofCSALTs 105
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Contents ix
7.3 OptimalDesignwithBudgetConstraints 106
7.3.1 SubjecttoSpecifiedBudgetandTerminationTime 107
7.3.2 SubjecttoStandardDeviationandTerminationTime 107
7.4 CaseStudieswithRCodes 108
7.5 SensitivityofOptimalDesigns 113
8 DesignofSimpleStep-StressAcceleratedLife-Tests 119
8.1 BriefOverview 119
8.2 One-ShotDeviceTestingDataUnderSimpleSSALTs 119
8.3 AsymptoticVariance 121
8.3.1 ExponentialDistribution 121
8.3.2 WeibullDistribution 122
8.3.3 WithaKnownShapeParameter𝑤 124
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8.3.4 WithaKnownParameterAboutStressLevel𝑤 125
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8.4 OptimalDesignofSimpleSSALT 126
8.5 CaseStudieswithRCodes 128
8.5.1 SSALTforExponentialDistribution 128
8.5.2 SSALTforWeibullDistribution 131
9 Competing-RisksModels 141
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9.1 BriefOverview 141
9.2 One-ShotDeviceTestingDatawithCompetingRisks 141
9.3 LikelihoodEstimationforExponentialDistribution 143
9.3.1 WithoutMaskedFailureModes 144
9.3.2 WithMaskedFailureModes 147
9.4 LikelihoodEstimationforWeibullDistribution 149
9.5 BayesianEstimation 155
9.5.1 WithoutMaskedFailureModes 155
9.5.2 LaplacePrior 156
9.5.3 NormalPrior 157
9.5.4 DirichletPrior 157
9.5.5 WithMaskedFailureModes 158
9.6 SimulationStudies 159
9.7 CaseStudywithRCodes 165
10 One-ShotDeviceswithDependentComponents 173
10.1 BriefOverview 173
10.2 TestDatawithDependentComponents 173
10.3 CopulaModels 174
10.3.1 FamilyofArchimedeanCopulas 175
10.3.2 Gumbel–HougaardCopula 176
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x Contents
10.3.3 FrankCopula 177
10.4 EstimationofDependence 180
10.5 SimulationStudies 181
10.6 CaseStudywithRCodes 184
11 ConclusionsandFutureDirections 187
11.1 BriefOverview 187
11.2 ConcludingRemarks 187
11.2.1 LargeSampleSizesforFlexibleModels 187
11.2.2 AccurateEstimation 188
11.2.3 GoodDesignsBeforeDataAnalysis 188
11.3 FutureDirections 189
11.3.1 WeibullLifetimeDistributionwithThresholdParameter 189
11.3.2 FrailtyModels 189
11.3.3 OptimalDesignofSSALTswithMultipleStressLevels 189
11.3.4 ComparisonofCSALTsandSSALTs 190
AppendixA DerivationofH(a,b) 191
i
AppendixB ObservedInformationMatrix 193
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AppendixC Non-IdentifiableParametersforSSALTsUnderWeibull
Distribution 197
AppendixD OptimalDesignUnderWeibullDistributionswithFixed
𝒘 199
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AppendixE ConditionalExpectationsforCompetingRisksModelUnder
ExponentialDistribution 201
AppendixF Kendall’sTauforFrankCopula 205
Bibliography 207
AuthorIndex 217
SubjectIndex 221
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xi
Preface
Lifetimeinformationobtainedfromone-shotdevicesisverylimitedastheentire
data are either left- or right-censored. For this reason, the analysis of one-shot
devicetestingdataposesaspecialchallenge.Thisbookprovidesseveralstatisti-
calinferentialmethodsforanalyzingone-shotdevicelifetimedataobtainedfrom
acceleratedlife-testsandalsodevelopsoptimaldesignsfortwomainstreamaccel-
erated life-tests – constant-stress and step-stress accelerated life-tests – that are
commonlyusedinreliabilitypractice.Thediscussionsprovidedinthebookwould
(cid:2) enablereliabilitypractitionerstobetterdesigntheirexperimentsfordatacollec- (cid:2)
tionfromefficientacceleratedlife-testswhentherearebudgetconstraintsinplace.
Thisisimportantfromestimationandpredictionpointofviewassuchoptimal
designswouldresultinasaccurateaninferenceaspossibleundertheconstraints
imposed on the reliability experiment. Moreover, R codes are presented within
eachchaptersothatuserscantryoutperformingtheirownanalysisonone-shot
devicetestingdata.
In addition, the inferential methods and the procedures for planning accel-
erated life-tests discussed in this book are not only limited to one-shot devices
alone but also can be extended naturally to accelerated life-tests with periodic
inspections (interval-censoring) and those with continuous monitoring and
censoring (right-censoring). The book finally concludes by highlighting some
important issues and problems that are worth considering for further research.
Thismaybeespeciallyusefulforresearchscholarsandnewresearchersinterested
intakingonthisinterestingandchallengingareaofresearchinreliabilitytheory
andpractice.
Itispossiblethatsomepertinentresultsorreferencesgotomittedinthisbook,
and we assure you that it is due to inadvertency on our part and not due to
scientific antipathy. We will appreciate greatly if the readers inform us of any
corrections/omissions, or any comments pertinent to any of the discussions in
thebook!
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xii Preface
OursincerethanksgototheentireWileyteam,Ms.MindyOkura-Marszycki,
Ms.KathleenSantoloci,andMr.BrettKurzman,fortakinggreatinterestinthis
project from day one, for all their help and encouragement during the whole
course,andfortheirfineassistanceduringthefinalproductionstageofthebook.
Ourthanksalsogotoourresearchcollaboratorsandgraduatestudentsfortheir
incisive comments and queries, which always benefited us greatly and helped
clarifysomeofourownideas!WeexpressoursincereappreciationtoMs.Elena
Maria Castilla Gonzalez, a doctoral student of Professor Leandro Pardo in the
Department of Statistics and Operations Research at Complutense University
ofMadrid,Spain,forhercarefulreadingofChapter5andalsoforsharingwith
ussomeRcodesthatshehaddevelopedconcerningrobustinferentialmethods
forone-shotdevicetestanalyses.Lastbutnotleast,ourspecialthanksgotoour
familiesfortheirpatienceandunderstanding,andforprovidingconstantsupport
andencouragementduringourworkonthisbook!
Finally, the first author (NB) wishes to state to his older daughter, Ms. Sarah
Balakrishnan, that though she lost out on getting his Volvo car due to a major
caraccident,sheshouldbeheartenedbythefactthattheaccidentresultedinthe
germinationofhisinterestandideasonone-shotdevices(airbags),andultimately
thisbooksolelydedicatedtothetopic!
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July,2020 NarayanaswamyBalakrishnan
ManHoLing
HonYiuSo
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