## 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 lend 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.

Original language | English (US) |
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Pages (from-to) | 339-368 |

Number of pages | 30 |

Journal | Probability in the Engineering and Informational Sciences |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - 2004 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Management Science and Operations Research
- Industrial and Manufacturing Engineering