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From differential to difference importance measures for Markov reliability models

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

Abstract

This paper presents the development of the differential importance measures (DIM), proposed recently for the use in risk-informed decision-making, in the context of Markov reliability models. The proposed DIM are essentially based on directional derivatives. They can be used to quantify the relative contribution of a component (or a group of components, a state or a group of states) of the system on the total variation of system performance provoked by the changes in system parameters values. The estimation of DIM at steady state using only a single sample path of a Markov process is also investigated. A numerical example of a dynamic system is finally introduced to illustrate the use of DIM, as well as the advantages of proposed evaluation approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:3:p:513-521
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    1. Marseguerra, M. & Zio, E. & Podofillini, L., 2005. "First-order differential sensitivity analysis of a nuclear safety system by Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 162-168.
    2. 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.
    3. Zio, Enrico & Podofillini, Luca, 2006. "Accounting for components interactions in the differential importance measure," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1163-1174.
    4. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    4. 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.
    5. Borgonovo, Emanuele & Aliee, Hananeh & Glaß, Michael & Teich, Jürgen, 2016. "A new time-independent reliability importance measure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 427-442.
    6. Mario Hellmich & Heinz-Peter Berg, 2013. "On the construction of component importance measures for semi-Markov systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 15-32, February.
    7. 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.
    8. Wu, Shaomin & Coolen, Frank P.A., 2013. "A cost-based importance measure for system components: An extension of the Birnbaum importance," European Journal of Operational Research, Elsevier, vol. 225(1), pages 189-195.
    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. 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.
    11. 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.
    12. Tyrväinen, T., 2013. "Risk importance measures in the dynamic flowgraph methodology," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 35-50.
    13. Borgonovo, E. & Smith, C.L., 2012. "Composite multilinearity, epistemic uncertainty and risk achievement worth," European Journal of Operational Research, Elsevier, vol. 222(2), pages 301-311.

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