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Numerical solution of reliability models described by stochastic automata networks

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  • Å nipas, Mindaugas
  • Radziukynas, Virginijus
  • ValakeviÄ ius, Eimutis
Abstract
This paper presents the solution of Markov chain reliability models with a large state-space. To specify a system reliability model, we use our previously proposed methodology, which is based on the Stochastic Automata Networks formalism. We model parts of the system by arrowhead matrices with functional transition rates. As a result, the infinitesimal generator matrix of the reliability model has a distinctive structure. In this paper, we demonstrate that a block Gauss–Seidel method can be applied very efficiently to such a structure. The application of the proposed methodology is illustrated by an example of a standard 3/2 substation configuration. Even though its Markov chain reliability model has almost two million states, its steady-state probabilities can be estimated in just a few seconds of CPU time.

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  • Å nipas, Mindaugas & Radziukynas, Virginijus & ValakeviÄ ius, Eimutis, 2018. "Numerical solution of reliability models described by stochastic automata networks," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 570-578.
    • Handle: RePEc:eee:reensy:v:169:y:2018:i:c:p:570-578
    DOI: 10.1016/j.ress.2017.09.024
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    References listed on IDEAS

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    1. Kim, Heungseob & Kim, Pansoo, 2017. "Reliability models for a nonrepairable system with heterogeneous components having a phase-type time-to-failure distribution," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 37-46.
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    5. Guo, Haitao & Yang, Xianhui, 2008. "Automatic creation of Markov models for reliability assessment of safety instrumented systems," Reliability Engineering and System Safety, Elsevier, vol. 93(6), pages 829-837.
    6. Jensen, H.A. & Muñoz, A. & Papadimitriou, C. & Millas, E., 2016. "Model-reduction techniques for reliability-based design problems of complex structural systems," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 204-217.
    7. 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.
    8. Å nipas, Mindaugas & Radziukynas, Virginijus & ValakeviÄ ius, Eimutis, 2017. "Modeling reliability of power systems substations by using stochastic automata networks," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 13-22.
    9. Cadini, Francesco & Agliardi, Gian Luca & Zio, Enrico, 2017. "Estimation of rare event probabilities in power transmission networks subject to cascading failures," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 9-20.
    10. Shijia Du & Lirong Cui & Cong Lin, 2016. "Some reliability indexes and sojourn time distributions for a repairable degradation model," Journal of Risk and Reliability, , vol. 230(3), pages 334-349, June.
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