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Efficient Monte Carlo methods for estimating failure probabilities

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  • Alban, Andres
  • Darji, Hardik A.
  • Imamura, Atsuki
  • Nakayama, Marvin K.

Abstract

We develop efficient Monte Carlo methods for estimating the failure probability of a system. An example of the problem comes from an approach for probabilistic safety assessment of nuclear power plants known as risk-informed safety-margin characterization, but it also arises in other contexts, e.g., structural reliability, catastrophe modeling, and finance. We estimate the failure probability using different combinations of simulation methodologies, including stratified sampling (SS), (replicated) Latin hypercube sampling (LHS), and conditional Monte Carlo (CMC). We prove theorems establishing that the combination SS+LHS (resp., SS+CMC+LHS) has smaller asymptotic variance than SS (resp., SS+LHS). We also devise asymptotically valid (as the overall sample size grows large) upper confidence bounds for the failure probability for the methods considered. The confidence bounds may be employed to perform an asymptotically valid probabilistic safety assessment. We present numerical results demonstrating that the combination SS+CMC+LHS can result in substantial variance reductions compared to stratified sampling alone.

Suggested Citation

  • Alban, Andres & Darji, Hardik A. & Imamura, Atsuki & Nakayama, Marvin K., 2017. "Efficient Monte Carlo methods for estimating failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 376-394.
    • Handle: RePEc:eee:reensy:v:165:y:2017:i:c:p:376-394
    DOI: 10.1016/j.ress.2017.04.001
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    1. Dube, Donald A. & Sherry, Richard R. & Gabor, Jeffery R. & Hess, Stephen M., 2014. "Application of risk informed safety margin characterization to extended power uprate analysis," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 19-28.
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    4. Grabaskas, Dave & Nakayama, Marvin K. & Denning, Richard & Aldemir, Tunc, 2016. "Advantages of variance reduction techniques in establishing confidence intervals for quantiles," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 187-203.
    5. Helton, Jon C., 2011. "Quantification of margins and uncertainties: Conceptual and computational basis," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 976-1013.
    6. Helton, Jon C. & Pilch, Martin & Sallaberry, Cédric J., 2014. "Probability of loss of assured safety in systems with multiple time-dependent failure modes: Representations with aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 171-200.
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