Efficient Monte Carlo methods for estimating failure probabilities

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

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)376-394
Number of pages19
JournalReliability Engineering and System Safety
StatePublished - Sep 1 2017

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Industrial and Manufacturing Engineering


  • Confidence intervals
  • Monte Carlo
  • Nuclear regulation
  • Probabilistic safety assessment
  • Risk analysis
  • Risk-informed safety-margin characterization
  • Structural reliability
  • Uncertainty
  • Variance reduction


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