Bayesian post-processing of Monte Carlo simulation in reliability analysis

Wolfgang Betz, Iason Papaioannou and Daniel Straub

Reliability Engineering and System Safety, 2022, vol. 227, issue C

Abstract: In reliability analysis with Monte Carlo simulation, the uncertainty about the probability of failure can be formally quantified through Bayesian statistics. Credible intervals for the probability of failure can be derived analytically. This paper gives a detailed overview of Bayesian post-processing for Monte Carlo simulation. We investigate the influence of different weakly-informative prior assumptions on the resulting credible intervals. On this basis, we recommend to use a prior distribution on the probability of failure that follows from the principle of maximum information entropy. We also show that even if no failure sample occurs in a Monte Carlo simulation, Bayesian post-processing still allows to deduce useful information about the probability of failure. The presented Bayesian post-processing strategy can also be applied if Monte Carlo simulation is used for reliability updating; i.e., to evaluate the probability of failure conditional on data or observations. We derive expectations for credible intervals for this case.

Keywords: Monte Carlo simulation; Bayesian post-processing; Credible intervals; Reliability analysis; Rare events; Reliability updating (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:227:y:2022:i:c:s0951832022003544

DOI: 10.1016/j.ress.2022.108731

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