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Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy

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  • Ad Ridder

Abstract

This paper reports simulation experiments, applying the cross entropy method such as the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failure biasing schemes that have been proved to give estimators with bounded relative errors. The results from the experiments indicate a considerable improvement of the performance of the importance sampling estimators, where performance is measured by the relative error of the estimate, by the relative error of the estimator, and by the gain of the importance sampling simulation to the normal simulation. Copyright Springer Science + Business Media, Inc. 2005

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  • Ad Ridder, 2005. "Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy," Annals of Operations Research, Springer, vol. 134(1), pages 119-136, February.
    • Handle: RePEc:spr:annopr:v:134:y:2005:i:1:p:119-136:10.1007/s10479-005-5727-9
    DOI: 10.1007/s10479-005-5727-9
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    References listed on IDEAS

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    1. Perwez Shahabuddin, 1994. "Importance Sampling for the Simulation of Highly Reliable Markovian Systems," Management Science, INFORMS, vol. 40(3), pages 333-352, March.
    2. G. Alon & D. Kroese & T. Raviv & R. Rubinstein, 2005. "Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment," Annals of Operations Research, Springer, vol. 134(1), pages 137-151, February.
    3. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    4. P. T. de Boer & D. P. Kroese & R. Y. Rubinstein, 2004. "A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks," Management Science, INFORMS, vol. 50(7), pages 883-895, July.
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    Cited by:

    1. Lirong Cui & Shijia Du & Aofu Zhang, 2014. "Reliability measures for two-part partition of states for aggregated Markov repairable systems," Annals of Operations Research, Springer, vol. 212(1), pages 93-114, January.
    2. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    3. Mattrand, C. & Bourinet, J.-M., 2014. "The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 171-182.
    4. Amarjit Budhiraja & Shu Lu & Yang Yu & Quoc Tran-Dinh, 2021. "Minimization of a class of rare event probabilities and buffered probabilities of exceedance," Annals of Operations Research, Springer, vol. 302(1), pages 49-83, July.
    5. Ali Kadhem, Athraa & Abdul Wahab, Noor Izzri & Aris, Ishak & Jasni, Jasronita & Abdalla, Ahmed N., 2017. "Computational techniques for assessing the reliability and sustainability of electrical power systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 1175-1186.

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