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Importance Sampling Simulations of Markovian Reliability Systems using Cross Entropy

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  • Ad Ridder

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

Abstract

This discussion paper resulted in a publication in the Annals of Operations Research (2005). Volume 134, issue 1, pages 119-136. 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 mea-sured 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.

Suggested Citation

  • Ad Ridder, 2004. "Importance Sampling Simulations of Markovian Reliability Systems using Cross Entropy," Tinbergen Institute Discussion Papers 04-018/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20040018
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    File URL: https://papers.tinbergen.nl/04018.pdf
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    References listed on IDEAS

    as
    1. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
    2. 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.
    3. Sandeep Juneja & Perwez Shahabuddin, 2001. "Fast Simulation of Markov Chains with Small Transition Probabilities," Management Science, INFORMS, vol. 47(4), pages 547-562, April.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    reliability; Markov chains; rare event simulation; importance sampling; cross entropy;
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