Reliability Prediction and Accelerated Testing

7ReliabilityPredictionandAcceleratedTestingE.A.Elsayed7.1IntroductionReliabilityisoneofthekeyqualitycharacteristicsofcomponents,productsandsystems.Itcannotbedirectlymeasuredandassessedlikeotherqualitycharacteris-ticsbutcanonlybepredictedforgiventimesandconditions.Itsvaluedependsontheuseconditionsoftheproductaswellasthetimeatwhichitistobepredicted.Reliabilitypredictionhasamajorimpactoncriticaldecisionssuchastheoptimumreleasetimeoftheproduct,thetypeandlengthofwarrantypolicyandassociateddurationandcost,andthedeterminationoftheoptimummaintenanceandreplace-mentschedules.Therefore,itisimportanttoprovideaccuratereliabilitypredictionsovertimeinordertodetermineaccuratelytherepair,inspectionandreplacementsstrategiesofproductsandsystems.Reliabilitypredictionsarebasedontestingasmallnumberofsamplesorproto-typesoftheproduct.Thedifficultyinpredictingreliabilityisfurthercomplicatedbymanylimitationssuchastheavailabletimetoconductthetestandbudgetcon-straints,amongothers.Testingproductsatdesignconditionsrequiresextensivetime,largenumberofunitsandcost.Clearlysomekindofreliabilitytesting,otherthantestingatnormaldesignconditions,isneeded.Oneofthemostcommonlyusedapproachesfortestingproductswithintheabovestatedconstraintsisacceleratedlifetesting(ALT)whereunitsorproductsaresubjectedtomoreseverestressconditionsthannormaloperatingconditionstoaccelerateitsfailuretimeandthenusethetestresultstopredict(extrapolate)thereliabilityatdesignconditions.ThisChapterwilladdressthedeterminationofoptimummaintenancescheduleatnormaloperatingconditionswhileutilizingtheresultsfromacceleratedtesting.WeclassifytheALTintotwotypes:acceleratedfailuretimetesting(AFTT)andaccelerateddegradationtesting(ADT).TheAFTTisconductedwhenacceleratedconditionsresultinthefailureoftestunitswithoutexperiencingfailuremechanismsdifferentfromthoseoccurringatnormaloperatingconditionsandwhenthereis“enough”unitstobetestedatdifferentconditions.Moreover,theeconomicsofconductingAFTTneedtobejustifiedasthetestisdestructiveanditsdurationis156E.Elsayeddirectlyrelatedtothereliabilityoftestunitsandtheappliedstresses.Finally,testingatstressesfarfromnormalmakesitdifficulttopredictreliabilityaccuratelyatnormalconditionsasinsomecasesfewornofailuresareobservedevenunderacceleratedconditionsmakingreliabilityinferenceviafailuretimeanalysishighlyinaccurate,ifnotimpossible.OntheotherhandADTisaviablealternativetoAFTTwhentheproduct’sphysicalcharacteristicsorperformanceindicesleadingtofailure(e.g.driftinresistancevalueofaresistor,changeinlightintensityoflightemittingdiodes(LED)andlossofstrengthofabridgestructure)experiencedegradationovertime.Moreover,significantdegradationdatacanbeobtainedbyobservingdegradationofasmallnumberofunitsovertime.Degradationtestingmayalsobeconductedeitheratnormaloracceleratedconditions,andnoactualfailureisrequiredforreliabilityinference(Liao2004).Inthischapter,weaddresstheissuesassociatedwithconductingacceleratedlifetestinganddescribehowthereliabilitymodelsobtainedfromALTareusedinthedeterminationoftheoptimummaintenanceschedulesatnormaloperatingconditions.Thischapterisorganizedasfollows.Section7.1providesanoverviewoftheroleofreliabilitypredictionandtheimportanceofacceleratedlifetesting.InSection7.2wepresentthetwomostcommonlyusedacceleratedlifetestingtypesinreliabilityengineering.TheapproachesandmodelsforpredictingreliabilityusingacceleratedlifetestingaredescribedinSection7.3whileSection7.4focusesonmathematicalformulationandsolutionofthedesignofacceleratedlifetestingplans.Section7.5showshowacceleratedlifetestingisrelatedtomaintenancedecisionsatnormaloperatingconditions.ModelstodeterminetheoptimumpreventivemaintenanceschedulesforbothfailuretimemodelsanddegradationmodelsarepresentedinSection7.6.AsummaryofthechapterispresentedinSection7.7.WebeginbydescribingtheALTtypes.7.2ALTTypes7.2.1AcceleratedFailureTimeTestingItisknownthatthemorereliablethedevice,themoredifficultitistomeasureitsreliability.Infact,manydeviceslastsolongthatlifetestingatnormaloperatingconditionsisimpractical.Furthermore,testingdevicesorcomponentsatnormaloperatingconditionsrequiresanextensiveamountoftimeandalargenumberofdevicesinordertoobtainaccuratemeasuresoftheirreliabilities.ALTiscommonlyusedtoobtainreliabilityandfailurerateestimatesofdevicesandcomponentsinamuchshortertime.Asimplewaytoacceleratethelifeofmanycomponentsorproductsthatareusedonacontinuoustimebasissuchastiresandlightbulbsistoacceleratetime(i.e.runtheproductatahigherusagerate).Itistypicallyassumedthatthenumberofcycles,hours,etc.,tofailureduringtestingisthesameaswouldbeobservedatthenormalusagerate.Forexample,inevaluatingthefailuretimedistributionoflightbulbswhichareusedontheaverageabout6hperday,oneyearofoperatingexperiencecanbecompressedintothreemonthsbyusingthelightbulbfor24heveryday.TheadvantageofthistypeoftestingisthatnoassumptionsneedtobeReliabilityPredictionandAcceleratedTesting157madeabouttherelationshipofthefailuretimedistributionsatboththeacceleratedandthenormalconditions.However,itisnotalwaystruethatthenumberofcyclestofailureathighusageratei