搜索
Chapter1:AnOverviewofWeibullAnalysis1-1Dr.RobertB.Abernethy•536OysterRoad,NorthPalmBeach,FL33408-4328•561-842-4082CHAPTER1.ANOVERVIEWOFWEIBULLANALYSIS1.1ObjectiveThishandbookwillprovideanunderstandingoflifedataanalysis.WeibullandLogNormalanalysiswillbeemphasizedparticularlyforfailureanalysis.Therearenewapplicationsofthistechnologyinmedicalanddentalimplants,warrantyanalysis,lifecyclecost,materialspropertiesandproductionprocesscontrol.Relatedquantitativemodelssuchasthebinomial,Poisson,Kaplan-Meier,GumbelextremevalueandtheCrow-AMSAAareincluded.TheauthorintendsthatanoviceengineercanperformWeibullanalysisafterstudyingthisdocument.Asecondaryobjectiveistoshowtheapplicationofpersonalcomputerstoreplacethelaborioushandcalculationsandmanualplottingrequiredinthepast.1.2BackgroundWaloddiWeibullinventedtheWeibulldistributionin1937anddeliveredhishallmarkAmericanpaperonthissubjectin1951.Heclaimedthathisdistributionappliedtoawiderangeofproblems.HeillustratedthispointwithsevenexamplesrangingfromthestrengthofsteeltotheheightofadultmalesintheBritishIsles.Heclaimedthatthefunction…maysometimesrendergoodservice.Hedidnotclaimthatitalwaysworked.TimehasshownthatWaloddiWeibullwascorrectinbothofthesestatements.HisbiographyisinAppendixN.Thereactiontohispaperinthe1950swasnegative,varyingfromskepticismtooutrightrejection.Theauthorwasoneoftheskeptics.Weibull'sclaimthatthedatacouldselectthedistributionandfittheparametersseemedtoogoodtobetrue.However,pioneersinthefieldlikeDorianShaininandLeonardJohnsonappliedandimprovedthetechnique.TheU.S.AirForcerecognizedthemeritofWeibull'smethodandfundedhisresearchuntil1975.Today,Weibullanalysisistheleadingmethodintheworldforfittingandanalyzinglifedata.DorianShaininintroducedtheauthortostatisticalengineeringattheHartfordGraduateCenter(RPI)inthemid-fifties.HestronglyencouragedtheauthorandPratt&WhitneyAircrafttouseWeibullanalysis.HewrotethefirstbookletonWeibullanalysisandproducedamovieonthesubjectforPratt&WhitneyAircraft.LeonardJohnsonatGeneralMotorsimprovedonWeibull'splottingmethods.Weibullusedmeanranksforplottingpositions.Johnsonsuggestedtheuseofmedianrankswhichareslightlymoreaccuratethanmeanranks.JohnsonalsopioneeredtheuseoftheBeta-BinomialconfidenceboundsdescribedinChapter7.E.J.GumbelshowedthattheWeibulldistributionandtheTypeIIISmallestExtremeValuesdistributionsarethesame.Healsoprovedthatifaparthasmultiplefailuremodes,thetimetofirstfailureisbestmodeledbytheWeibulldistribution.Thisistheweakest-link-in-the-chainconcept.Seepage1-12formoreonDorianShaininandE.J.Gumbel.WaloddiWeibull1887-1979PhotobySamC.Saunders1-2TheNewWeibullHandbookDr.RobertB.Abernethy•536OysterRoad,NorthPalmBeach,FL33408-4328•561-842-4082TheauthorfoundthattheWeibullmethodworkswithextremelysmallsamples,eventwoorthreefailuresforengineeringanalysis.Thischaracteristicisimportantwithaerospacesafetyproblemsandindevelopmenttestingwithsmallsamples.(Forstatisticalrelevance,largersamplesareneeded.)Advancedtechniquessuchasfailureforecasting,substantiationoftestdesigns,andmethodslikeWeibayesandtheDauserShiftweredevelopedbytheauthorandothersatPratt&Whitney.(Inretrospect,othersalsoindependentlyinventedsomeofthesetechniqueslikeWeibayesinthesametimeperiod.)Suchmethodsovercomemanydeficienciesinthedata.TheseadvancedmethodsandothersarepresentedinthisHandbook.1.3ExamplesThefollowingareexamplesofengineeringproblemssolvedwithWeibullanalysis:•Aprojectengineerreportsthreefailuresofacomponentinserviceoperationsduringathree-monthperiod.TheProgramManagerasks,Howmanyfailureswillwehaveinthenextquarter,sixmonths,andyear?Whatwillitcost?Whatisthebestcorrectiveactiontoreducetheriskandlosses?•Toordersparepartsandschedulemaintenancelabor,howmanyunitswillbereturnedtodepotforoverhaulforeachfailuremodemonth-by-monthnextyear?Theprogrammanagerwantstobe95%confidentthathewillhaveenoughsparepartsandlaboravailabletosupporttheoverallprogram.•AstateAirResourcesBoardrequiresafleetrecallwhenanypartintheemissionssystemexceedsa4%failurerateduringthewarrantyperiod.Basedonthewarrantydata,whichpartswillexceedthe4%rateandonwhatdate?•Afteranengineeringchange,howmanyunitsmustbetestedforhowlong,withoutanyfailures,toverifythattheoldfailuremodeiseliminated,orsignificantlyimprovedwith90%confidence?•Anelectricutilityisplaguedwithoutagesfromsuperheatertubefailures.Basedoninspectiondataforecastthelifeoftheboilerbasedonpluggingfailedtubes.Theboilerisreplacedwhen10%ofthetubeshavebeenpluggedduetofailure.•Thecostofanunplannedfailureforacomponent,subjecttoawearoutfailuremode,istwentytimesthecostofaplannedreplacement.Whatistheoptimalreplacementinterval?1.4ScopeWeibullanalysisincludes:•Plottingthedataandinterpretingtheplot•Failureforecastingandprediction•Evaluatingcorrectiveactionplans•Testsubstantiationfornewdesignswithminimumcost•Maintenanceplanningandcosteffectivereplacementstrategies•Sparepartsforecasting•Warrantyanalysisandsupportcostpredictions•Controllingproductionprocesses•Calibrationofcomplexdesignsystems,i.e.,CAD\CAM,finiteanalysis,etc.•RecommendationstomanagementinresponsetoserviceproblemsDatapr