TY - JOUR
T1 - Efficient Monte Carlo methods for estimating failure probabilities
AU - Alban, Andres
AU - Darji, Hardik A.
AU - Imamura, Atsuki
AU - Nakayama, Marvin K.
N1 - Funding Information:
This work has been supported in part by the National Science Foundation under Grants No. ?CMMI-1200065, DMS-1331010, and CMMI-1537322. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Also, additional funding came from a NJIT Provost Undergraduate Summer Research Fellowship.
Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2017/9/1
Y1 - 2017/9/1
N2 - 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.
AB - 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.
KW - Confidence intervals
KW - Monte Carlo
KW - Nuclear regulation
KW - Probabilistic safety assessment
KW - Risk analysis
KW - Risk-informed safety-margin characterization
KW - Structural reliability
KW - Uncertainty
KW - Variance reduction
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U2 - 10.1016/j.ress.2017.04.001
DO - 10.1016/j.ress.2017.04.001
M3 - Article
AN - SCOPUS:85018456910
SN - 0951-8320
VL - 165
SP - 376
EP - 394
JO - Reliability Engineering and System Safety
JF - Reliability Engineering and System Safety
ER -