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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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    8. 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.
    9. 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.
    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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