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QUICK SIMULATION METHODS FOR ESTIMATING THE UNRELIABILITY OF REGENERATIVE MODELS OF LARGE, HIGHLY RELIABLE SYSTEMS

Published online by Cambridge University Press:  01 July 2004

Marvin K. Nakayama  and
Perwez Shahabuddin
Marvin K. Nakayama
Affiliation:
Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, E-mail: [email protected]
Perwez Shahabuddin
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, E-mail: [email protected]
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Abstract

We investigate fast simulation techniques for estimating the unreliability in large Markovian models of highly reliable systems for which analytical/numerical techniques are difficult to apply. We first show mathematically that for “small” time horizons, the relative simulation error, when using the importance sampling techniques of failure biasing and forcing, remains bounded as component failure rates tend to zero. This is in contrast to naive simulation where the relative error tends to infinity. For “large” time horizons where these techniques are not efficient, we use the approach of first bounding the unreliability in terms of regenerative-cycle-based measures and then estimating the regenerative-cycle-based measures using importance sampling; the latter can be done very efficiently. We first use bounds developed in the literature for the asymptotic distribution of the time to hitting a rare set in regenerative systems. However, these bounds are “close” to the unreliability only for a certain range of time horizons. We develop new bounds that make use of the special structure of the systems that we consider and are “close” to the unreliability for a much wider range of time horizons. These techniques extend to non-Markovian, highly reliable systems as long as the regenerative structure is preserved.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 3 , July 2004 , pp. 339 - 368
Copyright
© 2004 Cambridge University Press

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