IntroductiontoReliabilityEngineering
ThirdEdition
JamesE.Breneman Manager,EngineeringTechnicalUniversity, Retired,Pratt&WhitneyCorporation DivisionofRaytheonTechnologies
ChittaranjanSahay ProfessorofMechanicalEngineering UniversityofHartford
ElmerE.Lewis ProfessorEmeritus DepartmentofMechanicalEngineering NorthwesternUniversity
Thiseditionfirstpublished2022 ©2022JohnWiley&Sons,Inc.Allrightsreserved.
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1st edition(9780471811992)1987,byJohnWiley&Sons,Inc. 2nd edition(9780471018339)1996,byJohnWiley&Sons,Inc.
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Names:Breneman,JamesE.,author.|Sahay,Chittaranjan, author|Lewis,E.E.(ElmerEugene),1938– author.
Title:Introductiontoreliabilityengineering/J.E.Breneman,DirectorofAdvancedEngineering ProcessesManager,EngineeringTechnicalUniversity,Retired,Pratt& WhitneyCorporation,ChittaranjanSahay,ProfessorofMechanical Engineering,UniversityofHartford,Hartford,Connecticut,ElmerE.Lewis,Professor Emeritus,DepartmentofMechanicalEngineering,NorthwesternUniversity, Evanston,Illinois.
Description:Thirdedition.|Hoboken,NJ:JohnWiley&Sons,Inc.,2022. |Includesbibliographicalreferencesandindex.
Identifiers:LCCN2021038736(print)|LCCN2021038737(ebook)|ISBN 9781119640561(cloth)|ISBN9781119640622(adobepdf)|ISBN 9781119640653(epub)
Subjects:LCSH:Reliability(Engineering)
Classification:LCCTA169.L472022(print)|LCCTA169(ebook)|DDC 620/.00452–dc23
LCrecordavailableathttps://lccn.loc.gov/2021038736
LCebookrecordavailableathttps://lccn.loc.gov/2021038737
Coverimage:©WikimediaCommons CoverdesignbyWiley
Setin9.5/12.5ptSTIXTwoTextbyStraive,Pondicherry,India
ToOurWivesandFamilies
Contents
Preface xv
AbouttheAuthor xix
AbouttheCompanionWebsite xxi
1Introduction 1
1.1ReliabilityDefined 1
1.2Performance,Cost,andReliability 2
1.3Quality,Reliability,andSafetyLinkage 4
1.4Quality,Reliability,andSafetyEngineeringTasks 6
1.5Preview 7
Bibliography 7
2ProbabilityandDiscreteDistributions 9
2.1Introduction 9
2.2ProbabilityConcepts 9
RelativeFrequency 9
Classical 10
Subjective 10
Samplespace (S)=setofallpossibleoutcomes 10
Outcome (e)=anelementofthesamplespace 10
Event =Asubsetofoutcomes 11
ProbabilityAxioms 11
MoreThanTwoEvents 17
CombinationsandPermutations 21
2.3DiscreteRandomVariables 23
PropertiesofDiscreteVariables 23
TheBinomialDistribution 26
ThePoissonDistribution 30
ConfidenceIntervals 33
MotivationforConfidenceIntervals 33
IntroductiontoConfidenceIntervals 35
BinomialConfidenceIntervals 37
CumulativeSumsofthePoissonDistribution(ThorndikeChart) 39
Bibliography 41
AdvancedtextsinProbability 41
Exercises 42
3TheExponentialDistributionandReliabilityBasics 47
3.1Introduction 47
3.2ReliabilityCharacterization 47 BasicDefinitions 48 TheBathtubCurve 50
3.3ConstantFailureRateModel 53 TheExponentialDistribution 54 DemandFailures 55 TimeDeterminations 57
3.4Time-DependentFailureRates 61
3.5ComponentFailuresandFailureModes 63 FailureModeRates 63 ComponentCounts 64
3.6Replacements 67
3.7Redundancy 71
ActiveandStandbyRedundancy 72
ActiveParallel 72 StandbyParallel 73 ConstantFailureRateModels 73
3.8RedundancyLimitations 75 Common-ModeFailures 76 LoadSharing 77 SwitchingandStandbyFailures 79 Cold,Warm,andHotStandby 80
3.9MultiplyRedundantSystems 81 1/N ActiveRedundancy 81
1/N StandbyRedundancy 83 m/N ActiveRedundancy 84
3.10RedundancyAllocation 86 High-andLow-levelRedundancy 88 FailSafeandFailtoDanger 90 VotingSystems 92
3.11RedundancyinComplexConfigurations 94 Series–ParallelConfigurations 94 LinkedConfigurations 96 Bibliography 98 Exercises 98 Redundancy 103
4ContinuousDistributions – Part1NormalandRelatedContinuousDistributions 109
4.1Introduction 109
4.2PropertiesofContinuousRandomVariables 109
ProbabilityDistributionFunctions 110 CharacteristicsofaProbabilityDistribution 112
SampleStatistics 114 TransformationsofVariables 115
4.3EmpiricalCumulativeDistributionFunction(EmpiricalCDF) 117
4.4UniformDistribution 120
4.5NormalandRelatedDistributions 122
TheNormalDistribution 123
NormalDistribution CautionsandWarnings!! 126
CentralLimitTheorem 127
CentralLimitTheoreminPractice 128
TheLognormalDistribution 128
LogNormalDistributionfromaPhysicsofFailurePerspective 134
4.6ConfidenceIntervals 135
PointandIntervalEstimates 135
EstimateoftheMean 139
4.7NormalandLognormalParameters 140
Bibliography 142
Exercises 143
5ContinuousDistributions – Part2WeibullandExtremeValueDistributions 149
5.1Introduction 149
The “WeakestLink” TheoryfromaPhysics-of-FailurePointofView 149
UsesofWeibullandExtremeValueDistributions 150
OtherConsiderations 151
AgeParametersandSampleSizes 151
EngineeringChanges,MaintenancePlanEvaluation,andRiskPrediction 152
WeibullswithCuspsorCurves 152
SystemWeibulls 153
NoFailureWeibulls 154
SmallSampleWeibulls 154
Summary 154
5.2StatisticsoftheWeibullDistribution 154
Weibull “Mathematics” 154
TheWeibullProbabilityPlot 158
ProbabilityPlottingPoints – MedianRanks 160
HowtoDoa “WeibullAnalysis” 161
WeibullPlotsandTheirEstimatesof β , η 163
TheThree-ParameterWeibullDidNotWork,WhatAreMyChoices? 167
TheDatahasa “Dogleg” BendorCuspWhenPlottedonWeibullPaper 167
SteepWeibullSlopes(β s)MayHideProblems 171
Low-TimeFailuresandCloseSerialnumbers – BatchProblems 172
Maximum-LikelihoodEstimatesof β and η 172
WeibayesAnalysis 176
WeibayesBackground(YouDoNotNecessarilyHaveAnyFailureTimes) 177
WeibullAnalysiswithFailuresOnlyandUnknownTimesontheUnfailedPopulation 180
ShiftingWeibullProcedure 180
ConfidenceBoundsandtheWeibullDistribution 181
ArbitraryCensoredData – Left-Censored,Right-Censored,andIntervalData 184
TheWeibullDistributioninaSystemofIndependentFailureModes 188
5.3ExtremeValueDistributions 189
5.4IntroductiontoRiskAnalysis 197
RiskAnalysis “Mathematics” 197
Bibliography 203
Contents
Exercises 205
Supplement1:WeibullDerivedfromWeakestLinkTheory 219
6ReliabilityTesting 221
6.1Introduction 221
6.2AttributeTesting(BinomialTesting) 223
TheClassicalSuccessRun 224
Zero-FailureAttributeTests 224
Non-Zero-FailureAttributeTests 225
6.3ConstantFailureRateEstimates 228
CensoringontheRight 228
MTTFEstimates 230
ConfidenceIntervals 232
6.4WeibullSubstantiationandReliabilityTesting 234
Zero-FailureTestPlansforSubstantiationTesting 235
WeibullZero-FailureTestPlansforReliabilityTesting 237
ReexpressionofaReliabilityGoaltoDetermine η 239
DesigningtheTestPlan 239
TestUnitswithCensoredTimes(duetoJuliusWang,Fiat-Chrysler) 241
TotalTestTime 242
WhyNotSimplyTesttoFailure? 243
6.5HowtoReduceTestTime 243
Run(Simultaneously)MoreTestSamplesThanYouIntendtoFail 243
SuddenDeathTesting 245
SequentialTesting 247
6.6NormalandLognormalReliabilityTesting 255
6.7AcceleratedLifeTesting 262
Compressed-TimeTesting 262
Advanced-StressTesting – LinearandAccelerationModels 265
LinearModelStressTesting 266
Advanced-StressTesting – AccelerationModels 270
TheArrheniusModel 270
TheInversePowerLawModel 275
OtherAccelerationModels 280
6.8Reliability-EnhancementProcedures 282
ReliabilityGrowthModelingandTesting 282
CalculationofReliabilityGrowthParameters 287
Goodness-of-FitTestsforReliabilityGrowthModels 288
ForTime-TerminatedTesting 288
ForFailure-TerminatedTesting 289
ForGroupedData 289
EnvironmentalStressScreening 299
What “Screens” areusedforESS? 302
ThermalCycling 302
RandomVibration 303
OtherScreens 303
HighlyAcceleratedLifeTests 304
HighlyAccelerated-StressScreening 305
Bibliography 305
Exercises 306
Supplement1:TablesforWeibullZero-failureSubstantiatioontesting 315
Supplement2:TablesForWeibullZer-failureSubstantiationtestingusing(t/Eta) 319
Supplement3:CriticalValuesforCramer–VonMisesGoodness-of-FitTest 323
Supplement4:OtherReliabilityGrowthModelsthathavebeenProposedandStudied (seeAFWAL-TR-84-2024fordetails) 323
(a)DeterministicModels 323
(b)PoissonProcessModels 324
(c)MarkovProcesses/TimeSeriesModels 325
Supplement5:Chi-SquareTable 326
7FailureModesandEffectsAnalysis – DesignandProcess 327
7.1Introduction 327
7.2FunctionalFMEA 328
7.3DesignFMEA 332
DesignFMEAProcedure 332
7.4ProcessFMEA(PFMEA) 339
7.5FMEASummary 349
Bibliography 350
Exercises 350
Supplement1:ShortcutTablesforStalledFMEATeams 359
Supplement2:FutureChangesinFMEAApproaches 360
Supplement3:DFMEAandPFMEAForms 360
8Loads,Capacity,andReliability 361
8.1Introduction 361
8.2ReliabilitywithaSingleLoading 362
LoadApplication 363 Definitions 364
8.3ReliabilityandSafetyFactors 368 NormalDistributions 368 LognormalDistributions 373 CombinedDistributions 374
8.4RepetitiveLoading 376 LoadingVariability 376 VariableCapacity 380
8.5TheBathtubCurve – Reconsidered 382
SingleFailureModes 383 CombinedFailureModes 385
Bibliography 387
Exercises 388
Supplement1:TheDiracDeltaDistribution 392
9MaintainedSystems 395
9.1Introduction 395
9.2PreventiveMaintenance 396
IdealizedMaintenance 396
ImperfectMaintenance 401
RedundantComponents 403
9.3CorrectiveMaintenance 403
Availability 404
Maintainability 405
9.4Repair:RevealedFailures 407
ConstantRepairRates 407
ConstantRepairTimes 410
9.5TestingandRepair:UnrevealedFailures 411
IdealizedPeriodicTests 411
RealPeriodicTests 413
9.6SystemAvailability 415
RevealedFailures 416
UnrevealedFailures 418
SimultaneousTesting 419
StaggeredTesting 420
Bibliography 422
Exercises 422
10FailureInteractions 427
10.1Introduction 427
10.2MarkovAnalysis 427
TwoIndependentComponents 429
Load-SharingSystems 432
10.3ReliabilityWithStandbySystems 434
IdealizedSystem 434
FailuresintheStandbyState 437
SwitchingFailures 439
PrimarySystemRepair 442
10.4MulticomponentSystems 444
MulticomponentMarkovFormulations 444
CombinationsofSubsystems 448
10.5Availability 449
StandbyRedundancy 449
SharedRepairCrews 453
MarkovAvailability – AdvantagesandDisadvantages 457
TheAdvantagesofMarkovAvailabilityAnalysis 457
TheDisadvantagesofMarkovAvailabilityAnalysis 457 Bibliography 457 Exercises 457
11SystemSafetyAnalysis 463
11.1Introduction 463
11.2ProductandEquipmentHazards 464
11.3HumanError 466
RoutineOperations 468
EmergencyOperations 470
11.4MethodsofAnalysis 471
FailureModes,Effects,andCriticalityAnalysis(FMECA) 472
Criticality 472
EventTrees 478
11.5FaultTrees 480
Fault-TreeConstruction 482
Nomenclature 483
FaultClassification 486
Primary,Secondary,andCommandFaults 486
PassiveandActiveFaults 486
FaultTreeExamples 487
DirectEvaluationofFaultTrees 494
QualitativeEvaluation 494
TopDown 495
BottomUp 495
LogicalReduction 496
QuantitativeEvaluation 496
ProbabilityRelationships 497
Primary-FailureData 498
Fault-TreeEvaluationbyCutSets 499
QualitativeAnalysis 499
MinimumCut-SetFormulation 499
Cut-SetDetermination 501
Cut-SetInterpretations 502
QuantitativeAnalysis 503
Top-EventProbability 503
Importance 505
Uncertainty 505
11.6Reliability/SafetyRiskAnalysis 505
Conclusion:AssumingWorstCasecanbeMisleading 508
AnotherApproach:MonteCarloSimulation 508
Bibliography 515
FMEA/FMECA 515
Exercises 516
AppendixA:UsefulMathematicalRelationships 521
A.1Integrals 521
DefiniteIntegrals 521
IntegrationbyParts 521
DerivativeofanIntegral 521
A.2Expansions 522
IntegerSeries 522
BinomialExpansion 522
GeometricProgression 522
InfiniteSeries 522
A.3SolutionofFirst-orderLinearDifferentialEquation 523
AppendixB:BinomialFailureProbabilityCharts 525
AppendixC: Ф(z):StandardNormalCDF 529
AppendixD:NonparametricMethodsandProbabilityPlotting 533
D.1Introduction 533
D.2NonparametricMethodsforProbabilityPlotting 533
BoxplotsandHistograms 533
Boxplot 533
Histogram 535
RankStatistics 536
D.3ParametricMethods 537
WeibullDistributionPlotting 540
Extreme-ValueDistributionPlotting 543
LognormalDistributionPlotting 545
D.4GoodnessofFit 547
Bibliography 555
3rdEdAnswerstoOdd – NumberedExercises 557
Index 607
Preface
Theobjectiveofthistextistoprovideanelementaryandreasonablyself-containedoverviewof reliabilityengineeringthatissuitableforanupper-levelundergraduateorfirst-yeargraduate courseforstudentsofanyengineeringdiscipline.Inaddition,thethirdeditionhasaddedmaterial forthe “beginning” reliabilityengineerwhoisinthefieldandtransferredtothereliability/safety discipline.Thematerialsreflecttheinherentlyinterdisciplinarycharacterofreliabilityconsiderationsandthecentralroleplayedbyprobabilityandstatisticalanalysisinpresentingreliabilityprinciplesandpractices.
Theexamplesandexercisesaredrawnfromavarietyofengineeringandsomenonengineering fields.Theycanbeunderstood,however,withonlytheknowledgefromthephysics,chemistry, andbasicengineeringcoursescontainedinthefirstyearsofnearlyallengineeringcurricula. Likewise,thereaderispresumedtohavecompletedonlythestandardmathematicssequence, throughordinarydifferentialequations,requiredofmostengineeringstudents.Nopriorknowledgeofprobabilityorstatisticsisassumed;thedevelopmentoftherequiredconceptsiscontained withinthetext.
Sincethesecondedition,atleasttwomajorchangeshavetakenplacethatareincorporated intothisnewedition.Thefirstistheincreasedindustrialemphasisonqualityintheproduct developmentcycleandthevitalrolethatreliabilityplaysinprovidinganoverallreliableandsafe product.Thesecondistherapidadvancesthathavetakenplaceinnotonlypersonalcomputer softwarebuttheextenttowhichthatsoftwarehaspenetratedtheengineeringprofessioninall arenas,thuslendingmoretimeforthinkingaboutthedataand thenthinking abouttheresultsof theanalysisratherthanspendingsomuchtime “computing” thesolutions.Thereaderwillfind manyinstancesinthiseditionwherecomputersoftwareisusednotonlytoproducesolutionsto specificproblemsbutalsotothegenerationoftablesofvalues(normalprobability,ttables,chisquaretables,etc.).
Foreachappropriateexampleinthisedition,thenecessarystepsforobtainingasolutionare indicatedusingreadilyavailablesoftware.EXCEL™ isaugmentedinmanycaseswithMINITAB® Thesetwoprogramswerechosenbecausetheyarewidelyavailable,andinstructionsfortheiruse arealsowidelyavailable.ThereareotherstatisticalsoftwarepackagesotherthanMINITABthat candomostoftheanalyses(SAS™,SAS/JMP™,RELIASOFT++™,SUPERSMITH™,andothers) thatarereferencedinthethirdedition.Theproblemsandsolutionsareamenabletoallthesesoftwarepackagesaswellasothers.
Anumberofadditionalimprovementshavebeenincorporatedintothenewedition.ReliabilityBasicsandtheExponentialDistributionareintroducedinChapter3;Chapter4,Continuous Distributions,Part1,introducesthenormalandlognormaldistributions.TheWeibulland extremevaluedistributionsaretreatedinChapter5,ContinuousDistributions,Part2. Chapter6isdedicatedtothetopicofreliabilitytesting.Itisexpandedfromthesecondedition toincludemanyoptionsforsettingupreliabilitytestingalongwiththeanalysisofthedata,thus emphasizingtheimportanceoftheWeibulldistributioninthepracticeofreliabilityengineering. Chapter7isdedicatedtoFMEA(FailureModesandEffectsAnalysis),anindispensabletoolin reliabilityinallareas,notjustdesignbutvirtuallyEVERYprocessinanyindustryincludingthe medicalandmost “soft” industriesintermsofprocessFMEA.Chapter8onLoads,Capacity,and Reliability;Chapter9onMaintainedSystems;andChapter10onFailureInteractionsarebasicallyunchangedfromthesecondedition.TwosectionshavebeenaddedtotheSystemSafety Analysis(nowChapter11)onFMECA(FailureModes,Effects,andCriticalityAnalysis)and SafetyRiskAnalysisandtheUseofMonteCarloSimulation.
Finally,thetextnowcontainsover150solvedexamplesandwellover300exercises,manyof whicharenew.Theanswerstotheodd-numberedexercisesaregivenattheendofthebook.
Thetextcontainsmorematerialthancanbetreatedindetailinanormalone-semesterundergraduatecourse,providingsomelatitudeinthetopicsthatmaybeemphasized.Ifthestudentshave hadsomepreviousexposuretoelementaryprobability,Chapter2canbesomewhattelescoped becausethoseprobabilityconceptsthataremorespecifictoreliabilityanalysisaresetforthin Chapter3.ThestatisticaltreatmentofdatacontainedmainlyinChapters4,5,6,and7isessential toawell-roundedundergraduatecourseinreliabilityengineering.Thematerialsintheremaining chaptersmaybecoveredindependentlyinanadvancedundergraduateorgraduatecourse.For example,thequantitativeanalysisoftheeffectsofloadandcapacitiescontainedinChapter8is criticaltotheunderstandingoffailuremechanisms,butthereliabilitysystemsconsiderationsconcentratedinChapters9and11maybereadindependentlyofit.Finally,thesystemsafetyanalysis containedinChapter11maybeunderstoodwithoutfirstcoveringtheMarkovanalysismethods developedinChapter10.
Inadditiontothecontinuedthanksowedtothestudentsandcolleagueswhoprovidedtheir adviceandassistancewithpreviouseditions,wewouldliketoacknowledgethehelpofspecific individualsinencouragingtheauthorstoincludethereliabilityengineeringprofessionalsinthis book’sprospectiveaudience:
Mysincerethanksto:
AswellasthestudentsatNorthwesternUniversitywhohaveferretedouterrorsinthefirsteditionandmadeconstructivecriticismsandsuggestionsforimprovements.GeorgeCoonsofthe MotorolaCorporationhasbeenparticularlyhelpfulinprovidingmaterialsandsuggestionsrelated tothetreatmentofqualityissues,andJimLookabaughofNorthwesterndesignedthedataacquisitionsystemandobtainedthelightbulbreliabilityresultsthatserveasthebasisforseveralexamplesinChapters5and8.Finally,Iwouldliketoexpressmyappreciationforthecontinued understandingofmywifeandchildrenwhileImonopolizedthefamilycomputer.
ElmerLewis
Mysincerethanksto:
• allmycolleaguesatPratt&Whitney,especiallyDr.BobAbernethy,WesAnnas,DaveMcDermott,SteveLuko,andinparticular,myP&WEngineeringmentorJackSammons,withoutwhose
encouragementIwouldnothaveexploredtheneedsatP&WinWeibullRisk&Reliability Analysis.
• ManyformerUTCdivisions(Carrier,Otis,andSikorsky)andmanyothercompaniesIhave consultedforaswellasuniversitystudentswhohadthefortitudetolistentomyadviceandtake themanyReliability,Statistics,andSafetycoursesIhavetaught – thanksforhelpingmebecome abetterlistenerandteacher.
• MySAE,ASA,andASQprofessionalassociateshaveprovidedmewiththeirideasandsupport:in particular,WesFulton,PaulBarringer,JimMcLinn,andTrevorCraney.
JimBreneman
Prof.AlanHadadandDr.LouisManzionefortheirsupportinalwayshelpingmepursuemy goals.Myportionofthematerialsinthebookareinfluencedbydiscussionswithmystudentsover theyearsattheUniversityofHartfordandtheStateUniversityofNewYorkatBinghamton. Ireceivedencouragementfrommyteacher,Prof.RajendraDubeyoftheUniversityofWaterloo. Iamgratefultomyindustrycollaboratorswhohavetransformedmyapproachtoengineering education.Inparticular,JimBreneman,coauthorofthebook,wasaninspirationwhileserving asthepointofcontactforUniversityrelationsatPrattandWhitney.Iowethemostofthanks tomywife,SaraswatiSahay,andmychildren,whostoodbymeandhelpedmestayfocused.
ChittaranjanSahay
JimBreneman,Vergennes,VT,USA ChittaranjanSahay,WestHartford,CT,USA ElmerLewis,Evanston,IL,USA December2021 Preface
AbouttheAuthor
JamesE.Breneman,receivedaB.S.inmathematicsfromUniversityofNorthCarolina,ChapelHill, andanM.S.inmathematicsandstatisticsfromN.C.State,Raleigh,NorthCarolina.Heservedin theUSArmyduringtheVietnamwarandisaformerdirectorofAdvancedEngineeringProcesses andthefounderandmanagerofPratt&Whitney’sEngineeringTechnicalUniversity.Hehas workedover45yearsinthereliabilityandstatisticalarenaand35yearsatPratt&Whitney (DivisionofRaytheonTechnologies)inreliabilityandsafetyriskanalysis.HeisaPratt&Whitney FellowaswellasSAEFellowinreliability,arecipientoftheASQGrantmedal,andotherprofessionalawards.HeisacoauthoroftheUSAFWeibullAnalysisHandbookandnumerous(published andunpublished)papersandhandbooksinreliabilityandsafety.Heisaconsultanttovarious aerospaceandnonaerospaceindustriesintheareasofreliability,statistics,andrisk.
ChittaranjanSahay,ReceivedaB.Sc.inMechanicalEngineeringfromRegional(now,National) InstituteofTechnology,JamshedpurinIndia,andaPh.D.fromIndianInstituteofTechnology, Delhi,India.Hewasapost-doctoralfellowattheUniversityofWaterlooandUniversityof OttawainCanadabeforemovingtotheStateUniversityofNewYorkatBinghamton.Hehas servedasVisitingFacultyatCornellUniversity,BirlaInstituteofTechnology,MesraRanchias B.M.BirlaProfessorofMechanicalEngineering,andatIndianInstituteofTechnology,Patna. HeisaFellowoftheAmericanSocietyofMechanicalEngineers.HeistheVernonD.Roosa DistinguishedProfessorofManufacturingEngineering,aprofessorofMechanicalEngineering, andtheDirectorforCenterofmanufacturingandMetrologyattheUniversityofHartford.
ElmerE.LewisisprofessoremeritusandformerchairmanoftheDepartmentofMechanical Engineering,NorthwesternUniversity.HereceivedhisB.S.inengineeringphysicsandanM.S.and Ph.D.innuclearengineeringattheUniversityofIllinois,Urbana.HeservedasacaptainintheUS ArmyandasaFordFoundationfellowandanassistantprofessoratMITbeforejoiningNorthwestern’sfaculty.HehasalsoheldappointmentsasvisitingprofessorattheUniversityofStuttgartand guestscientistattheNuclearResearchCenteratKarlsruhe,Germany,andhasservedasaconsultanttoArgonne,LosAlamos,andOakRidgeNationalLaboratoriesandtoanumberofindustrial firms.AfellowoftheAmericanNuclearSocietyandwinnerofitsEugeneP.WignerReactorPhysics andArthurHollyComptonAwards,hisresearchhasbeenfocusedonreliabilitymodeling,radiationtransport,andthephysicsandsafetyofnuclearsystems.Heistheauthororcoauthorofover 200publicationsincludingtheWileybooks, NuclearPowerReactorSafety,ComputationalMethods ofNeutronTransport,andthefirsttwoeditionsof IntroductiontoReliabilityEngineering
AbouttheCompanionWebsite
Thisbookisaccompaniedbyacompanionwebsite:
www.wiley.com/go/breneman/relabilityengineering3e
Theinstructorsitewillinclude:
• Answerstoend-of-chapterexercises
• PowerPoints
• Projectideas
Thestudentsitewillinclude:
• Excelfilesoftheexercises
“Whenanengineer,followingthesafetyregulationsoftheCoastGuardortheFederal AviationAgency,translatesthelawsofphysicsintothespecificationsofasteamboatboiler orthedesignofajetairliner,heismixingsciencewithagreatmanyotherconsiderationsall relatingtothepurposestobeserved.Anditisalwayspurposesintheplural aseriesof compromisesofvariousconsiderations,suchasspeed,safetyeconomyandsoon.”
Source:D.KPrice,TheScientificEstate,1968
1.1ReliabilityDefined
Theworlddemandsthattheperformanceofproductsandsystemsbeimprovedwhileatthesame timereducingtheircost.Therequirementtominimizetheprobabilityoffailures,whetherthose failuressimplyincreasecostsandirritationorgravelythreatenthepublicsafety,hasplaced increasedemphasisonreliabilityandsafety.Theformalbodyofknowledgethathasbeendevelopedforanalyzingsuchfailuresandminimizingtheiroccurrencecutsacrossvirtuallyallengineeringdisciplines,providingtherichvarietyofcontextsinwhichreliabilityconsiderationsappear. Indeed,deeperinsightintofailuresandtheirpreventionistobegainedbycomparingandcontrastingthereliabilitycharacteristicsofsystemsofdifferingcharacteristics:computers,electromechanicalmachinery,energyconversionsystems,chemicalandmaterialsprocessingplants,and structures,tonameafew.
Inthebroadestsense,reliabilityisassociatedwithdependability,withsuccessfuloperation,and withtheabsenceofbreakdownsorfailures.Itisnecessaryforengineeringanalysis,however,to definereliabilityquantitativelyasaprobability.
Thus, reliabilityisdefinedastheprobabilitythatasystemwillperformitsintendedfunctionfora specifiedperiodoftimeunderagivensetofconditions.Systemisusedhereinagenericsensesothat thedefinitionofreliabilityisalsoapplicabletoallvarietiesofproducts,subsystems,equipment, components,andparts.
Aproductorsystemissaidtofailwhenitceasestoperformitsintendedfunction.Whenthereisa totalcessationoffunction – anenginestopsrunning,astructurecollapses,apieceofcommunicationequipmentgoesdead – thesystemhasclearlyfailed.Often,however,itisnecessarytodefine failurequantitativelyinordertotakeintoaccountthemoresubtleformsoffailure,throughdeteriorationorinstabilityoffunction.Thus,amotorthatisnolongercapableofdeliveringaspecified torque,astructurethatexceedsaspecifieddeflection,apartthatisseriouslycorrodedoreroded(yet
stillworking),oranamplifierthatfallsbelowastipulatedgainhasfailed.Intermittentoperationor excessivedriftinelectronicequipmentandthemachinetoolproductionofout-of-toleranceparts mayalsobedefinedasfailures.
Thewayinwhichtimeisspecifiedinthedefinitionofreliabilitymayalsovaryconsiderably, dependingonthenatureofthesystemunderconsideration.Forexample,inanintermittentlyoperatedsystemonemustspecifywhethercalendartimeorthenumberofhoursofoperationistobe used.Iftheoperationiscyclic,suchasthatofaswitch,timeislikelytobecastintermsofthenumberofoperations.Somesubsystemsofthesamesystem(e.g.jetengine)mayhavedifferenttime criteriathatdrivestheirfailure.Ifreliabilityistobespecifiedintermsofcalendartime,itmayalso benecessarytospecifythefrequencyofstartsandstopsandtheratioofoperatingtototaltime.
Inadditiontoreliabilityitself,otherquantitiesareusedtocharacterizethereliabilityofasystem. Themeantimetofailureandfailurerateareexamples,andinthecaseofrepairablesystems,soalso aretheavailabilityandmeantimetorepair.Thedefinitionoftheseandothertermswillbeintroducedasneeded.
1.2Performance,Cost,andReliability
Muchofengineeringendeavorisconcernedwithdesigningandbuildingproductsforimproved performance.Westriveforlighterandthereforefasteraircraft,forthermodynamicallymoreefficientenergyconversiondevices,forfastercomputers,andforlarger,longerlastingstructures.The pursuitofsuchobjectives,however,oftenrequiresdesignsincorporatingfeaturesthatmoreoften thannotmaytendtobelessreliablethanolder,lowerperformancesystems,atleastinitiallywhen thecustomerreceivesthem.Thetrade-offsbetweenperformance,reliability,andcostareoftensubtle,involvingloading,systemcomplexity,andtheemploymentofnewmaterialsandconcepts.
Loadismostoftenusedinthemechanicalsenseofthestressonastructure.Buthereweinterpret itmoregenerallysothatitalsomaybethethermalloadcausedbyhightemperature,theelectrical loadonagenerator,oreventheinformationloadonatelecommunicationssystem.Whateverthe natureoftheloadonasystemoritscomponentsmaybe,performanceisfrequentlyimproved throughincreasedloading.Thus,byincreasingtheweightofanaircraft,weincreasethestress levelsinitsstructure;bygoingtohigher – thermodynamicallymoreefficient – temperatureswe areforcedtooperatematerialsunderconditionsinwhichthereareheat-inducedlossesofstrength andmorerapidcorrosion/erosion.Byallowingforever-increasingflowsofinformationincommunicationssystems,weapproachthefrequencylimitsatwhichswitchingorotherdigitalcircuitsmay operate.
Asthephysicallimitsofsystemsortheircomponentsareapproachedinordertoimproveperformance,thenumberoffailuresincreaseunlessappropriatecountermeasuresaretaken.Thus, specificationsforapurermaterial,tighterdimensionaltolerance,andahostofothermeasures arerequiredtoreduceuncertaintyintheperformancelimitsandtherebypermitonetooperate closetothoselimitswithoutincurringanunacceptableprobabilityofexceedingthem(i.e.failure). Butintheprocessofdoingso,thecostofthesystemislikelytoincrease.Eventhen,adverseenvironmentalconditions,productdeterioration,andmanufacturingflawsallleadtohigherfailure probabilitiesinsystemsoperatingneartheirlimitloads.
Systemperformancemayoftenbeincreasedattheexpenseofincreasedcomplexity,thecomplexityusuallybeingmeasuredbythenumberofrequiredcomponentsorparts.Onceagain,reliability willbedecreasedunlesscompensatingmeasuresaretaken,foritmaybeshownthatifnothingelse
