• Journal of Applied Optics
  • Vol. 43, Issue 4, 635 (2022)
Zhicao ZHAO, Hui WU, Fengzhu ZHENG, Wenbo ZHANG, and Guan WANG
Author Affiliations
  • [in Chinese]
  • show less
    DOI: 10.5768/JAO202243.0401007 Cite this Article
    Zhicao ZHAO, Hui WU, Fengzhu ZHENG, Wenbo ZHANG, Guan WANG. Reliability modeling and analysis method for electro-optical system with multiple failure modes[J]. Journal of Applied Optics, 2022, 43(4): 635 Copy Citation Text show less

    Abstract

    The system reliability modeling and analysis is the basis of reliability allocation and prediction, fault tree analysis and reliability optimization design. A reliability modeling and analysis method for electro-optical system was introduced. For some subsystems with multiple failure modes following exponential distribution, according to the homogeneous Markov stochastic process theory, a reliability model was built using the Markov state transition diagram method. Then the analytical expression, numerical calculation method and Monte Carlo simulation method were presented. The reliability model was applied to an example analysis for power supply circuit of an airborne electro-optical system. The above methods were used to calculate, and the results were compared and analyzed, which verifies the correctness and feasibility of the proposed method.
    A=[n(λ1+λ2)nλ1000nλ20(n1)(λ1+λ2)(n1)λ100(n1)λ2000(λ1+λ2)λ1λ2000000000000](1)

    View in Article

    {P0'(t)=n(λ1+λ2)P0(t)P1'(t)=nλ1P0(t)(n1)(λ1+λ2)P1(t)Pn1'(t)=2λ1Pn2(t)(λ1+λ2)Pn1(t)Pn'(t)=λ1Pn1(t)Pf'(t)=nλ2P0(t)+(n1)λ2P1(t)++λ2Pn1(t)(2)

    View in Article

    {P0*(s)=1s+n(λ1+λ2)P1*(s)=nλ1s+(n1)(λ1+λ2)P0*(s)Pn1*(s)=2λ1s+(λ1+λ2)Pn2*(s)Pn*(s)=1sλ1Pn1*(s)Pf*(s)=1s(nλ2P0*(s)+(n1)λ2P1*(s)++λ2Pn1*(s))(3)

    View in Article

    Rs(t)=i=0n1Pi(t)=1Pn(t)Pf(t)(4)

    View in Article

    P(t)P(n)=P(0)Pm(Δt)(5)

    View in Article

    P(Δt)=[1n(λ1+λ2)Δtnλ1Δt000nλ2Δt01(n1)(λ1+λ2)Δt(n1)λ1Δt00(n1)λ2Δt0001(λ1+λ2)Δtλ1Δtλ2Δt000000000000](6)

    View in Article

    MTTF=T¯=1Nl=1NTl(7)

    View in Article

    σMTTF=1N1l=1N(TlT¯)2(8)

    View in Article

    [T¯z1α/2σMTTFN,T¯+z1α/2σMTTFN](9)

    View in Article

    P(Δt)=[13(λ1+λ2)Δt3λ1Δt003λ2Δt012(λ1+λ2)Δt2λ1Δt02λ2Δt001(λ1+λ2)Δtλ1Δtλ2Δt0000000000](10)

    View in Article

    Rs(t)=λ12λ1λ2+λ22(λ1+λ2)2e3(λ1+λ2)t+3λ1(λ2λ1)(λ1+λ2)2e2(λ1+λ2)t+3λ12(λ1+λ2)2e(λ1+λ2)t(11)

    View in Article

    MTTF=0+Rs(t)=5.5λ12+3.5λ1λ2+λ223(λ1+λ2)3(12)

    View in Article

    z1α/2σMTTFT¯N1%(13)

    View in Article

    Rss(t)=e3(λ1+λ2)t3e2(λ1+λ2)t+3e(λ1+λ2)t(14)

    View in Article

    MTTFs=0+Rss(t)=5.53(λ1+λ2)=30000h(15)

    View in Article

    Rsp(t)=e3(λ1+λ2)t(16)

    View in Article

    MTTFp=0+Rsp(t)=13(λ1+λ2)=5455.55h(17)

    View in Article

    Zhicao ZHAO, Hui WU, Fengzhu ZHENG, Wenbo ZHANG, Guan WANG. Reliability modeling and analysis method for electro-optical system with multiple failure modes[J]. Journal of Applied Optics, 2022, 43(4): 635
    Download Citation