weibull_statistical_properti-2

weibull_statistical_properti-2

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1、页码,1/3Home>TheWeibullDistribution>WeibullStatisticalPropertiesWeibullStatisticalPropertiesTheMeanorMTTFThemean,,(alsocalledMTTForMTBFbysomeauthors)oftheWeibullpdfisgivenby:(3)whereisthegammafunctionevaluatedatthevalueof.Thegammafunctionisdefinedas:Thisfunctioni

2、sprovidedwithinWeibull++forcalculatingthevaluesofΓ(n)atanyvalueofn.ThisfunctionislocatedintheQuickStatisticalReferenceofWeibull++.Forthetwo-parametercase,Eqn.(3)canbereducedto:NotethatsomepractitionerserroneouslyassumethatηisequaltotheMTBForMTTF.Thisisonlytruef

3、orthecaseofβ=1sinceTheMedianThemedian,,isgivenby:(4)TheModeThemode,,isgivenby:(5)TheStandardDeviationThestandarddeviation,σ,isgivenby:T页码,2/3TheWeibullReliabilityFunctionTheequationforthethree-parameterWeibullcumulativedensityfunction,cdf,isgivenby:Recallingtha

4、tthereliabilityfunctionofadistributionissimplyoneminusthecdf,thereliabilityfunctionforthethree-parameterWeibulldistributionisgivenby:TheWeibullConditionalReliabilityFunctionThethree-parameterWeibullconditionalreliabilityfunctionisgivenby:(6)or:Eqn.(6)givesthere

5、liabilityforanewmissionoftduration,havingalreadyaccumulatedThoursofoperationuptothestartofthisnewmission,andtheunitsarecheckedouttoassurethattheywillstartthenextmissionsuccessfully.Itiscalledconditionalbecauseyoucancalculatethereliabilityofanewmissionbasedonthe

6、factthattheunitorunitsalreadyaccumulatedThoursofoperationsuccessfully.TheWeibullReliableLifeThereliablelife,T,ofaunitforaspecifiedreliability,startingthemissionatagezero,isgivenby:R(7)ThisisthelifeforwhichtheunitwillbefunctioningsuccessfullywithareliabilityofR(

7、T).IfR(T)=0.50thenRR,themedianlife,orthelifebywhichhalfoftheunitswillsurvive.TheWeibullFailureRateFunctionTheWeibullfailureratefunction,λ(T),isgivenby:页码,3/3SeeAlso:TheWeibullDistributionGotoweibull.comGotoReliaSoft.com©1996-2006.ReliaSoftCorporation.ALLRIGHTSR

8、ESERVED.

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