可能性概率Probability

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1、ProbabilitymultiplicationPFD=PD(A∩B)=PD(A)*PD(B)ABPDUPDUPDDPDD共因系数b诊断覆盖率DCABPSUPSUPSDPSD共因系数b诊断覆盖率DCPFD=PD(A∩B)=PD(A)+PD(B)–PD(A∩B)PFS=PS(A∪B)=PS(A)+PS(B)-PD(A)*PD(B)ProbabilitymultiplicationPFD=P(A∩B)+P(B∩C)+P(A∩C)A1A2B1B2诊断覆盖率DC诊断覆盖率DC未诊断率1-DCFunctionalsafetyEngineering-ProbabilityProbabi

2、lityRulesofProbabilityTypesofEventProbabilitymultiplicationProbabilityadditionFaultTreesProbabilityAssignmentProbabilityassignedbytwomethods:PhysicalpropertydeterminationGeometry,physicalshapeExperimentaloutcomedeterminationNumberofoccurrences/NumberofTrialsProbabilityisanumber:(0

3、bilityP(Gold)=0.8FunctionalsafetyP(Mable)=0.75EventTypesIndependent–EventsthatdonotaffecteachotherCoinTossesDiceThrowsComplimentary–Whenoneoutcomedoesnotoccur,theotherwillalwaysoccurCoinMutuallyExclusive–WhenoneeventoccurtheothercannothappenDiceIndependentEventsEventsthatdonoteffecteachothe

4、rTossingoftwocoinsThrowingapairofdiceFailureofonecomponentinasystem?NormallyconsideredindependentComplimentaryEventsComplimentaryWhenoneoutcomedoesnotoccur,theotherwillalwaysoccurTossingacoinTwoeventspossible–headandtailsSuccess/Failure?ProbabilityofComplementaryEventsP(A*)=1–P(A)Probabilit

5、yofsuccessfuloperationforthenextyearis0.8.Whatistheprobabilityoffailurethenextyear?(0,2)MutuallyExclusiveEventsMutuallyExclusiveWhenoneeventoccurtheothercannothappenTossofonedieOutcomeof1,2,3,4,5,6aremutuallyexclusiveProbabilitymultiplicationP(AANDB)=P(A)*P(B)ABProbabilitymultiplicationForI

6、ndependenteventsP(AANDB)=P(A)*P(B)LimitSwitchSolenoidValveInthenextyear,theprobabilityofsuccessfuloperationforalimitswitchis0.9andtheprobabilityofsuccessfuloperationforasolenoidvalveis0.98.Whatistheprobabilityofsuccessforthesystemconsistingofbothelements?LimitswitchANDsolenoideP(A)*P(B)=0.9

7、*0.98=0.882ProbabilityAdditionMutuallyExclusiveEventsP(AorB)=P(A)+P(B)ABProbabilityAdditionMutuallyExclusiveEventsP(AorB)=P(A)+P(B)Roll1die.Whatistheprobabilityofgettinga4ora6?Probabilityofgetting4->1/6Probabilityofgetting6->1/6Theprobabilityofrolling4OR