可靠性與系統(tǒng)工程學(xué)院生專業(yè)課課件-維修性設(shè)計分析

維修性設(shè)計與分——模馬爾可夫過程–系統(tǒng)各部件的 馬爾可夫過程或在(t,t+馬爾可夫過程應(yīng)用-定義狀態(tài)變量1X(t)1

ttp0(t)P{X(t)0};p1(t)P{X(t)馬爾可夫過程應(yīng)用-單部件系狀態(tài)轉(zhuǎn)移過程（Δt時間001P01(Δt)=P11(Δt)=1-P00(Δt)=1-轉(zhuǎn)移概率：P10ΔtμΔt+0P01(Δt)=λΔt+0數(shù)學(xué)處P(Tt)P(t)1ep00(t)P{X(tt)0X(t)0}e 1t0 (t)P{X(tt) X(t)0}1ett0 (t)P{X(tt)0X(t)1}1ett0pp(t)P{X(tt)1X(t)1}et1t0馬爾可夫過程應(yīng)用-單部件系狀態(tài)概P0(t+Δt)=P0(t)P00(Δt)+P1(t)=(1-λΔt)P0(t)+μΔtP1(t+Δt)=P0(t)P01(Δt)+P1(t)=(1-λΔt)P0(t)+μΔt馬爾可夫過程應(yīng)用-單部件系整理pp(t) 0tp0(tt)p0(t)0(t)p(t1p(t) 1tp1(tt)p1(t)p0(t)p(t1popo(01,p100sp0(s)p0(0)po(s)p1(s)sp1(s)p1(0)po(s)p1(s) 代入初始條件，經(jīng)整理 (s )p0(s) p1(s p0(s)(s)p1(s) p(s)

s

s

1

s s

s(s) s 對上式作拉氏反變換，得pp(t) ()0epp(t)1p(t) (1e()t)10馬爾可夫過程應(yīng)用-單部件系系統(tǒng)可用AA(t)p(t) 0 ()eAAlimA(t) t馬爾可夫過程應(yīng)用-單部件系建模過程的簡化001P01(Δt)=P11(Δt)=1-P00(Δt)=1-馬爾可夫過程應(yīng)用-單部件系μ流μλ λ流 流馬爾可夫過程應(yīng)用-單部件系μμλ λ p0p0(t)p0(t)p1(tp1(t)p0(t)p1(t馬爾可夫過程應(yīng)用-單部件系p0p0(t) p0(t) p1(t)p1p0(tpp1(t) p0(t) p1(t) p0 p0 馬爾可夫過程應(yīng)用-可修串率分別為λ1λ2，維修率為μ1μ1。當(dāng)馬爾可夫過程應(yīng)用-可修串定義狀態(tài)變量XX(t)狀態(tài)pp0(t)P{X(t)0};p1(t)P{X(t)1};p2(t)P{X(t)馬爾可夫過程應(yīng)用-可修串10102μ1馬爾可夫過程應(yīng)用-可修串μ1 22pp0(t)(12)p0(t)1p1(t)2p2(tp1(t)1p0(t)1p1(tp2(t)2p0(t)2p2(tpp0(0)=1,馬爾可夫過程應(yīng)用-可修串 [1] (21)p0 1p 2p2 和2pp002p2p0p p2 馬爾可夫過程應(yīng)用-可修串A=(1+2λ/μ)-馬爾可夫過程應(yīng)用-可修并都發(fā)生故障，系停止工作待修。馬爾可夫過程應(yīng)用-可修并定義X(t)X(t)狀態(tài)pp0(t)P{X(t)0};p1(t)P{X(t)1};p2(t)P{X(t)馬爾可夫過程應(yīng)用-可修并狀態(tài)轉(zhuǎn)0101λ2馬爾可夫過程應(yīng)用-可修并聯(lián)

p0(t)2p0(t)p1(t)2 p0(t)(

p1(t)p1(t)p2(tp2(t)

p0(t)p2(t

pp0(0)=1,馬爾可夫過程應(yīng)用-可修并A(t)=p0(t)+p1(t)=1- 222 22 2p p 2 p ( )p p p0(t p2(tp0p1p2馬爾可夫過程應(yīng)用-馬爾可夫過程應(yīng)用-定義變狀態(tài)變量X(t)

作狀態(tài)pp0(t)P{X(t)0};p1(t)P{X(t)1};p2(t)P{X(t)馬爾可夫過程應(yīng)用-狀態(tài)轉(zhuǎn)01012馬爾可夫過程應(yīng)用-修表決系統(tǒng)

p0(t)3p0(t)

p1(tp1(t)3 p0(t)(2)p1(t)p2(tp2(t)2 p0(t)p2(t

pp0(0)=1,馬爾可夫過程應(yīng)用-A(t)=p0(t)+p1(t)=1-AA326 32 3p p 2 p (2 )p p 2 pp0p1p2

(t) p

(t不用時間定義的如如何理解可靠性中“規(guī)定的時間”通常通常時間含義：如工作小時（MTBF）、日歷時不用時間定義的fN3不用時間定義的射2 2發(fā)數(shù)

A=（N1+N2+f)/(N1+N2+N3+N4+MRBF——平均故障間隔發(fā)數(shù)（相當(dāng)N——每次連發(fā)平均r——單位時間的平均射M——修復(fù)時間（相當(dāng)

示例某機(jī)槍系統(tǒng)的MRBF=100發(fā)，MTTR=0.5解戰(zhàn)備完好率概率情況設(shè)定——裝備具有自測試功概率PPOR(td)R(t)FDRM(tmtd)[1R(t)]確定戰(zhàn)備完好率例.TT(解PPOR(0.5)R(1)FDRM(tmtd0.5)[10.8