,,泊松分布,,,,,

,,5.3.8PoissonDistribution,,,,PAGE108,

,Thisdistributionisusedquitefrequentlyinreliabilityanalysis.Itcanbeconsideredanextension,,,,,,

,"ofthebinomialdistributionwhennisinfinite.Infact,itisusedtoapproximatethebinomial",,,,,,

,distributionwhenn≥20andp≤0.05.,,,,,,

,"IfeventsarePoissondistributed,theyoccurataconstantaveragerateandthenumberofevents",,,,,,

,occurringinanytimeintervalareindependentofthenumberofeventsoccurringinanyother,,,,,,

,"timeinterval.Forexample,thenumberoffailuresinagiventimewouldbegivenby",,,,,,

,"這種分布是可靠性分析中很常用的一種分布形式,右以把這種分布認(rèn)為是當(dāng)N為無限大時(shí)的二項(xiàng)分布的擴(kuò)展.",,,,,,

,"事實(shí)上,當(dāng)N大于等于20,P大于等于0.05,這種分布用來近似表示二項(xiàng)分布.",,,,,,

,"如果事件是泊松分布的,它們以恒定的平均變化率出現(xiàn),并且在任一時(shí)間間隔中,事件出現(xiàn)的次數(shù)與在任一其它時(shí)間間隔出現(xiàn)",,,,,,

,"的事件次數(shù)無關(guān).如,在某一給定時(shí)間的故障數(shù)將由下式給出:",,,,,,

,wherexisthenumberoffailuresandaistheexpectednumberoffailures.,,,,,,

,"式中X是故障數(shù),A是期望的故障數(shù).用于可靠性分析時(shí),該式成為:",,,,,,

,where:,,,,,,

,λ=failurerate,,,,故障率,,

,t=lengthoftimebeingconsidered,,,,考慮的時(shí)間長度,,

,x=numberoffailures,,,,故障數(shù),,

,在T時(shí)刻可靠度函數(shù)R(t)或零故障概率由下式給出:,,,,,,

,,,,,"這是我們的老朋友,指數(shù)分布",,

,"對余度設(shè)備來說,R(t)可以用在t時(shí)刻γ次或更少次故障的概率,在那種情況下:",,,,,,

,,,,,,,gg

,示例:,,,,,,

,有允許失效數(shù)的示例:,,,,,,

,"民兵導(dǎo)彈發(fā)射控制臺(tái)的平均失效率為每小時(shí)0.001次指示燈失效.如查指示燈的失效不能超過2,那么該控制臺(tái)工作500小時(shí)的可靠度",,,,,,

,是多少?,,,,,,

,,λ=0.001t=500λt=0.5r≤2,,,,,

,,,,,,,,

,余度系統(tǒng)示例,,,,,,

,"設(shè)由10個(gè)單元組成的局部余度系統(tǒng).假如每次發(fā)生故障立即修好或更換,可預(yù)期每小時(shí)平均故障數(shù)為λ.試求出當(dāng)系統(tǒng)工作t小時(shí)",,,,,,

,的單元平均故障數(shù).,,,,,,

,因有:,f(x)=(exp(-λt)*(λt)^x)/x!,,,,,

,"當(dāng)系統(tǒng)有N個(gè)這樣的單元,則在T小時(shí)平均故障數(shù)為Nλt.",,,,,,

,,f(x)=exp(-nλt)*(nλt)^x/x!,,,,,

,如果參數(shù)如下則:,,,,,,

,,λ,0.001,,,0,

,,t,50,,x=,1,

,,n,10,,,2,

,,f(x=0)=p(0),0.60653066,,,,

,,f(x=1)=p(1),0.30326533,,,,

,,f(x=2)=p(2),0.075816332,,,,

,則該系統(tǒng)正常工作50小時(shí)而單元發(fā)生故障的概率是0.607;而在單元故障數(shù)不大于1時(shí)的概率是0.91(P(0)和P(1)的總數(shù)),,,,,,

,"在任務(wù)期間發(fā)生兩次或更多次故障的機(jī)會(huì)是9%,如果系統(tǒng)有9個(gè)單元正常工作,并且如果進(jìn)一步允許我們在任務(wù)期間對一個(gè)",,,,,,

,"單元