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Probabilistic model–based multi-integration formulas for quantifying a generalized minimal cut sequence

Author

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  • Daochuan Ge
  • Ruoxing Zhang
  • Qiang Chou
  • Yanhua Yang

Abstract

Many sequence- and function-dependent failure behaviors may exist in fault-tolerant systems, in which the failure of the systems depends not only on the combination of basic events but also on their failure sequences. Such systems can be modeled by dynamic fault tree with Priority AND gate, Spare gate, Sequence Enforcing gate and Functional Dependence gate. The existing analytical methods for analyzing these dynamic gates are mainly Markov-based or inclusion–exclusion-based approaches. Compared with Markov approaches, the inclusion–exclusion-based method presents notable advantages. However, to the author’s knowledge, no references by far have presented general multi-integration formulas applicable for solving a generalized minimal cut sequence, which is an unavoidable problem in inclusion–exclusion-based method. In this article, new multi-integration formulas are proposed based on traditional probabilistic models, which are applicable for solving a generalized minimal cut sequence as well as any dynamic gate. The rigorous derivation processes are given. The application and advantages of our proposed approach are demonstrated through a case study and the results indicate our proposed approach is reasonable.

Suggested Citation

  • Daochuan Ge & Ruoxing Zhang & Qiang Chou & Yanhua Yang, 2015. "Probabilistic model–based multi-integration formulas for quantifying a generalized minimal cut sequence," Journal of Risk and Reliability, , vol. 229(1), pages 73-82, February.
    • Handle: RePEc:sae:risrel:v:229:y:2015:i:1:p:73-82
    DOI: 10.1177/1748006X14552004
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    References listed on IDEAS

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    1. Xing, Liudong & Shrestha, Akhilesh & Dai, Yuanshun, 2011. "Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1375-1385.
    2. Durga Rao, K. & Gopika, V. & Sanyasi Rao, V.V.S. & Kushwaha, H.S. & Verma, A.K. & Srividya, A., 2009. "Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment," Reliability Engineering and System Safety, Elsevier, vol. 94(4), pages 872-883.
    3. Merle, G. & Roussel, J.-M. & Lesage, J.-J., 2011. "Algebraic determination of the structure function of Dynamic Fault Trees," Reliability Engineering and System Safety, Elsevier, vol. 96(2), pages 267-277.
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    Cited by:

    1. Ge, Daochuan & Lin, Meng & Yang, Yanhua & Zhang, Ruoxing & Chou, Qiang, 2015. "Quantitative analysis of dynamic fault trees using improved Sequential Binary Decision Diagrams," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 289-299.
    2. Gascard, Eric & Simeu-Abazi, Zineb, 2018. "Quantitative Analysis of Dynamic Fault Trees by means of Monte Carlo Simulations: Event-Driven Simulation Approach," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 487-504.
    3. Son, Kwang Seop & Kim, Dong Hoon & Kim, Chang Hwoi & Kang, Hyun Gook, 2016. "Study on the systematic approach of Markov modeling for dependability analysis of complex fault-tolerant features with voting logics," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 44-57.

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