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Bayesian post-processing of Monte Carlo simulation in reliability analysis

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  • Betz, Wolfgang
  • Papaioannou, Iason
  • Straub, Daniel

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.

Suggested Citation

  • Betz, Wolfgang & Papaioannou, Iason & Straub, Daniel, 2022. "Bayesian post-processing of Monte Carlo simulation in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:reensy:v:227:y:2022:i:c:s0951832022003544
    DOI: 10.1016/j.ress.2022.108731
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    References listed on IDEAS

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    1. Kelly, Dana L. & Smith, Curtis L., 2009. "Bayesian inference in probabilistic risk assessment—The current state of the art," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 628-643.
    2. Janssen, Hans, 2013. "Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 123-132.
    3. Cho, Jaehyun & Kim, Yochan & Kim, Jaewhan & Park, Jinkyun & Kim, Dong-San, 2020. "Realistic estimation of human error probability through Monte Carlo thermal-hydraulic simulation," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Smith, Curtis & Kelly, Dana & Dezfuli, Homayoon, 2010. "Probability-informed testing for reliability assurance through Bayesian hypothesis methods," Reliability Engineering and System Safety, Elsevier, vol. 95(4), pages 361-368.
    5. Gribok, Andrei & Agarwal, Vivek & Yadav, Vaibhav, 2020. "Performance of empirical Bayes estimation techniques used in probabilistic risk assessment," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    6. Papaioannou, Iason & Geyer, Sebastian & Straub, Daniel, 2019. "Improved cross entropy-based importance sampling with a flexible mixture model," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
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    2. Jia-Qi, Liu & Yun-Wen, Feng & Da, Teng & Jun-Yu, Chen & Cheng, Lu, 2023. "Operational reliability evaluation and analysis framework of civil aircraft complex system based on intelligent extremum machine learning model," Reliability Engineering and System Safety, Elsevier, vol. 235(C).

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