Estimation of Degradation-Based Reliability in Out

EstimationofDegradation-BasedReliabilityinOutdoorEnvironmentsVictorChanandWilliamQ.MeekerDepartmentofStatisticsIowaStateUniversityAmes,IA50011July19,2001AbstractSomeimportantreliabilityproblemsinvolveestimatingalifedistributionwhenfailureisduetochemicaldegradationofmaterialsorproductsthatareexposedtotheoutdoorenvironment.Thereisagrowingneedtoobtaintimelypredictionsofsuchdegradationbehaviorsonthebasisofacceleratedlaboratorytests.Laboratorylifetestsprovideinfor-mationaboutdegradationprocesses.Historicalweatherdataareusedtocharacterizethestochasticoutdoorenvironmentovertime.Aphysical/chemicalmodelfordegradationrateisusedasabasisforusingthesedatatoproducereliabilityestimates.Weproposeandillustratetheuseofanevaluation/estimationmethodthatinvolvestimeseriesmodeling.Themethodisillustratedwithanexampleinvolvingthedegradationofasolar-reflectormaterial.Wewillalsoshowhowtoconstructapproximateconfidenceintervalsforimpor-tantreliabilitymetrics.Keywords:ServiceLifePrediction,TimeSeries,AcceleratedTesting,RiskAssess-ment.11Introduction1.1MotivationSomeimportantreliabilityapplicationsinvolvequantifyingtheservicelifeofmaterialsandproductsthataresubjectedtohighlyvariableenvironmentalvariableslikeoutdoortemperatureorsolarradiation.Thephysicalstateorperformanceoftheseproductscanoftenbecharacterizedormeasuredasafunctionoftime.Inotherwords,itispossibletomeasurethephysicaldegradationorwear-and-tearoftheproductsastheyageandmovetowardeventualfailure.Examplesofsuchproductsincludeautomotivepaintsandcoatings,whosefailureiscausedbydegradationrelatedtolong-termweathering(i.e.,exposuretooutdoorenvironmentalelements).Commonmeasuresofdegradationforpaintsandcoatingsincludeglosslossandcolorchange.Conventionalmethodologiesfortheservicelifepredictionofpaintandcoatingproductshave,forthepast80years,typicallyreliedonacceleratedoutdoortests(Pearceetal.,1954;Martin,1999).Suchtestsareexpensiveandtime-consuming.Attemptshavealsobeenmadetocorrelatetheresultsfromlaboratorytestswithoutdoorexposuredata.Thesemethodshave,however,oftenbeenunsuccessfulinpredictingcoatingfailuresoreveninrankingalternativeformulations.Thelackoftimelyandaccuratepredictionshaveprovedtobeverycostlytobothmanufacturersandconsumers.Systematicapproachesbasedonmechanisticmodelsofdegradationhavebeenproposedtoimprovethecurrentstateofreliabilityestimationofthematerialsexposedtotheoutdoorenvironment(e.g.Martin,1999;Meeker,Escobar,andChan,2001;PickettandGardner,2001).Theseapproachesinvolvecharacterizingtheenvironmentstochasticallyanddeter-miningtheeffectsofenvironmentalvariablesonthedegradationorfailuremechanisms,bothofwhicharethenrelatedthroughacumulativedamageordegradationmodel.Thismodelisthenusedtoestimatethereliabilityortomakeservicelifepredictionsofthematerialsintheirintendedserviceenvironment.Thispaperproposesastatisticalmethodologytoestimatedegradation-basedreliabilityofsuchmaterialswithintheframeworkofthenewapproach.1.2GoalQuantifyingthereliabilityofmaterialsorproductssuchaspaintsandcoatingsinvolvesthepredictionofthelevelofdegradationresultingfromexposureovertime,takingintoaccounttherandomnatureoftheoutdoorenvironment.Withthisinmind,themain2objectiveofthemethodologypresentedinthispaperistoestimatethefollowing:1.Theprobabilitydistributionofcumulativedegradationatagivenpointintime.2.Theprobabilitydistributionoffailuretime,or“crossingtime”,(i.e.,thetimeatwhichthecumulativedegradationreachesacriticallevel).Thecriticallevelofdegradationdefinesthefailureevent.Notethatthesetwodistributionsarisefromtherandomnessintheenvironment.Theyallowustoconductriskassessmentofthefailureofthematerialexposedtooutdoorweatheringandtocharacterizeitsreliabilityorservicelifeprediction.1.3RelatedWorkMostoftheliteratureonmethodsforreliabilityanalysisfocusesonfailuretimemodels.Thereisonlyalimitedamountofliteratureondegradation-basedreliabilityanalysis.DiscussiononthissubjectcanbefoundinChapter11ofNelson(1990),Chapter7ofTobiasandTrindade(1995),andChapters13and21ofMeekerandEscobar(1998).Workoncumulativedamagemodelshasbeenmoreextensive.GertsbakhandKor-donsky(1969)presentanearlyworkonsuchmodels.AsurveyofthedevelopmentsofmodelsandpertinentreferencesaregivenbySaunders(1982).Somerelevantworkofin-terestonfailuremodelsbasedoncumulativedamageofmaterialsincludesSaunders(1970),BogdanoffandKozin(1985),andGillenandCelina(2001).BauerandMartin(1999)andBauerandMartin(2001)describerecentworkontheservicelifepredictionassociatedwithpaintsandcoatingsexposedtotheoutdoorenvi-ronment,includingphysicalandchemicalstudiesofthedegradationofsuchmaterials.Martinetal.(1996)presentandcomparetheservicelifepredictionmethodologiesusedinthecoatingsindustrywiththoseusedinotherindustries,wheresuchmethodshavebeenmoresuccessful.Thefieldofreliabilityandsurvivalanalysisinhighlyvariableenvironmentsiscurrentlyunderdeveloped,withitsliteraturesscatteredwidelyinvariousdifferentfields.Anoverviewofalargeclassoffailureandcumulative-exposuremodelsbasedonstochasticprocesses,withanemphasisonprobabilisticmodeling,isgivenbySingpurwalla(1995).Thispaperalsoprovideskeyreference