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Reliability importance analysis of Markovian systems at steady state using perturbation analysis

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  • Do Van, Phuc
  • Barros, Anne
  • Bérenguer, Christophe

Abstract

Sensitivity analysis has been primarily defined for static systems, i.e. systems described by combinatorial reliability models (fault or event trees). Several structural and probabilistic measures have been proposed to assess the components importance. For dynamic systems including inter-component and functional dependencies (cold spare, shared load, shared resources, etc.), and described by Markov models or, more generally, by discrete events dynamic systems models, the problem of sensitivity analysis remains widely open. In this paper, the perturbation method is used to estimate an importance factor, called multi-directional sensitivity measure, in the framework of Markovian systems. Some numerical examples are introduced to show why this method offers a promising tool for steady-state sensitivity analysis of Markov processes in reliability studies.

Suggested Citation

  • Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2008. "Reliability importance analysis of Markovian systems at steady state using perturbation analysis," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1605-1615.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:11:p:1605-1615
    DOI: 10.1016/j.ress.2008.02.020
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    References listed on IDEAS

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    1. Paul Glasserman & Sridhar Tayur, 1995. "Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems," Management Science, INFORMS, vol. 41(2), pages 263-281, February.
    2. Paul Glasserman, 1992. "Derivative Estimates from Simulation of Continuous-Time Markov Chains," Operations Research, INFORMS, vol. 40(2), pages 292-308, April.
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    Cited by:

    1. Do, Phuc & Bérenguer, Christophe, 2020. "Conditional reliability-based importance measures," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Shumin Li & Shubin Si & Liudong Xing & Shudong Sun, 2014. "Integrated importance of multi-state fault tree based on multi-state multi-valued decision diagram," Journal of Risk and Reliability, , vol. 228(2), pages 200-208, April.
    3. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    4. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    5. Rocco S., Claudio M. & Emmanuel Ramirez-Marquez, José, 2015. "Assessment of the transition-rates importance of Markovian systems at steady state using the unscented transformation," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 212-220.
    6. Borgonovo, E., 2010. "The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 485-495, August.
    7. E. Borgonovo & C. L. Smith, 2011. "A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA," Operations Research, INFORMS, vol. 59(6), pages 1461-1476, December.
    8. C M Rocco S, 2012. "Effects of the transition rate uncertainty on the steady state probabilities of Markov models using interval arithmetic," Journal of Risk and Reliability, , vol. 226(2), pages 234-245, April.
    9. Aizpurua, J.I. & Catterson, V.M. & Papadopoulos, Y. & Chiacchio, F. & D'Urso, D., 2017. "Supporting group maintenance through prognostics-enhanced dynamic dependability prediction," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 171-188.
    10. P Do Van & A Barros & C Berenguer, 2008. "Importance measure on finite time horizon and application to Markovian multistate production systems," Journal of Risk and Reliability, , vol. 222(3), pages 449-461, September.
    11. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    12. Zhai, Qingqing & Yang, Jun & Xie, Min & Zhao, Yu, 2014. "Generalized moment-independent importance measures based on Minkowski distance," European Journal of Operational Research, Elsevier, vol. 239(2), pages 449-455.
    13. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe, 2010. "From differential to difference importance measures for Markov reliability models," European Journal of Operational Research, Elsevier, vol. 204(3), pages 513-521, August.
    14. Claudio M Rocco S, 2013. "Affine arithmetic for assessing the uncertainty propagation on steady-state probabilities of Markov models owing to uncertainties in transition rates," Journal of Risk and Reliability, , vol. 227(5), pages 523-533, October.
    15. Tyrväinen, T., 2013. "Risk importance measures in the dynamic flowgraph methodology," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 35-50.

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