Introduction to Reliability

Copyright©2004reliabilitysolutionsallrightsreservedIntroductiontoReliabilityWhatisReliability?Copyright©2004reliabilitysolutionsallrightsreserved•ReliabilityistheprobabilityadeviceorsystemwillNOTfailtoperformitsintendedfunction(s)duringaspecifiedtimeintervalwhenoperatedunderstatedconditions.R(t)=Reliability=1-ProbabilityofFailure=1-F(t)TheBathtubCurveCopyright©2004reliabilitysolutionsallrightsreservedTheBathtubCurveCopyright©2004reliabilitysolutionsallrightsreserved•BathtubCurveismadeupofthreefailuredistributions•Early•Chance/Random(Intrinsic)•Wearout•EachhasadifferentWeibullslopeparameter•Early1•Intrinsic=1•Wearout1DescribingtheFailureModelCopyright©2004reliabilitysolutionsallrightsreserved•Weibulldistributioncanbeusedtomodelfailurepatternswithincreasingordecreasingfailurerates.•Increasingfailurerateshaveslopeparameters1,decreasingis1.•ExponentialisatypeofWeibullwithparameter=1•Weibullplotssimple,butpowerfulDescribingtheFailureModelCopyright©2004reliabilitysolutionsallrightsreserved•Exponentialdistributionusedtomodelaconstantprobabilityoffailure•WiththeExponential,unfailedunitsare‘goodasnew’failurebehaviourisnotdependentonpasthistoryEXPONENTIALFAILURELAW:F=1–e-λtλ=failurerate,t=elapsedtimeDescribingtheFailureModelCopyright©2004reliabilitysolutionsallrightsreserved-Normaldistributionisanappropriatemodelforcomponentsinwhichfailureiscausedbysomeformofwearingeffect(AutoTyres,etc)DescribingtheFailureModelCopyright©2004reliabilitysolutionsallrightsreservedLog–NormalLookslikethenormaldistribution,butisskewedtotheright.Usedtomodelproportionaleffects,suchas“failureoccurswhenasoldercrackgrowstoacertainpoint”.Threeparameterdistributionwithmean,varianceandlevelofskewness.DescribingtheFailureModelCopyright©2004reliabilitysolutionsallrightsreserved•WearoutFailuresfailduetogradualdeteriorationbymechanical,physicalorchemicalpropertiessuchascorrosionorelectro-migration•Whenitemsfailbecauseofwearout,theageoftheunitisimportantasyoungerunitshavehigherreliabilitythanoldones.•Wearoutfailuresbelongtothemainfailuredistribution.DistributionofComponentStrengthsCopyright©2004reliabilitysolutionsallrightsreservedTrimodalDistribution•Oftenanewproductwilldisplaythreedifferentfailuredistributions-InfantMortality-FreakPopulation-mainPopulation•Testinghasshowneachtohavefollowingcontentwithrespecttototalfailure-InfantMortality0.1-5%-Freakpopulation2-20%-mainPopulation85%•Qualityobjectivetoremovefirst2distributionspriortoshipmentSystemReliabilityPredictionsCopyright©2004reliabilitysolutionsallrightsreservedRELIABILITYOFSERIESSYSTEMS•Systemwillfailifanyoneoftheunitsfails•SystemisnomorereliablethanitsweakestcomponentForasystemwith‘N’components,eachhavingreliability‘P’Rs=P1xP2xP3xP4………………xPnP1P2P3P4PnSystemReliabilityPredictionsCopyright©2004reliabilitysolutionsallrightsreservedPARALLELSYSTEMS•Systemwillnotfailwiththefailureofonecomponent•RedundantcomponentswillperformfunctionoffailedcomponentRs=1–UnreliabilityRs=1–(U1xU2xU3……….xUn)P1P2P3P4PnSystemReliabilityPredictionsCopyright©2004reliabilitysolutionsallrightsreservedRELIABILITYOFSERIESSYSTEMSEXAMPLE1ThreecomponentsA,B,Chavereliabilitiesof0.92,0.95and0.96Thesystemreliabilityis:Rs=PAxPBxPC=0.92x0.95x0.96=0.839SystemReliabilityPredictionsCopyright©2004reliabilitysolutionsallrightsreservedRELIABILITYOFSERIESSYSTEMSEXAMPLE2Aseriessystemiscomposedoffourcomponentswithfailureratesof0.002,0.001,0.0025and0.0005The100hoursystemreliabilityis:Rt=e–tλxe–tλxe–tλxe–tλ-100(0.002+0.001+0.0025+0.0005)R(100)=e=0.5488SystemReliabilityPredictionsCopyright©2004reliabilitysolutionsallrightsreservedRELIABILITYOFPARALLELSYSTEMSEXAMPLE1ThreecomponentsA,B,Chavereliabilitiesof0.92,0.95and0.96Thesystemreliabilityis:Rs=1-[(1–Pa).(1–Pb).(1–Pc)]=0.99984EXAMPLE2Asystemhas100componentsBranchAhas20partswithRa=0.95BranchBhas20partswithRb=0.93BranchChas60partswithRc=0.96Ra=(Pa)N=(0.95)20=0.358Ub=1–(0.93)20=0.766Uc=1–(0.96)60=0.914Ubc=Ub.Uc=0.914x0.766=0.700Rbc=1–Ubc=0.300Rs=Ra.Rbc=(0.358).(0.300)=0.107BCAPredictingtheFailurePatternCopyright©2004reliabilitysolutionsallrightsreservedINTRODUCTION•Importanttodefinedistributiontocorrectlypredictfailurepattern•Normalandexponentialdistributionswidelyused-Normaltodescribewearout-Exponentialtodescribelongtermintrinsicfailurepattern•NeedtodistinguishbetweenbothPredictingtheFailurePatternCopyright©2004reliabilitysolutionsallrightsreserved1.NORMALDISTRIBUTION•Modelsfailurescausedbywearingeffect•Examplebasedonfailuredistributionofmechanicalbearings-Meantimetofailure=1000hrs-standarddeviationis=100hrs•NormaldistributiontablesusedtodefinefailureprobabilityCopyright©2004reliabilitysolutionsallrightsreserved0.000.010.020.030.040.050.060.070.080.090.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.53590.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.57530.20.57930.58320.58710.59100.57480.59870.60260.60640.61030.61410.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.65170.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.68790.50.69150.69500.69850.70190.70540