Efficient Monte Carlo methods for estimating failure probabilities

Document Type

Article

Publication Date

9-1-2017

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.

Identifier

85018456910 (Scopus)

Publication Title

Reliability Engineering and System Safety

External Full Text Location

https://doi.org/10.1016/j.ress.2017.04.001

ISSN

09518320

First Page

376

Last Page

394

Volume

165

Grant

CMMI-1200065

Fund Ref

National Science Foundation

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