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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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    Citations

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    Cited by:

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    3. He, Zhichao & Wang, Yanhui & Xia, Weifu & Shen, Yue & Hao, Yucheng & Ren, Qiuyang, 2023. "A method for reliability assessment of complex electromechanical system based on improved network connectivity entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    4. Martón, I. & Sánchez, A.I. & Carlos, S. & Mullor, R. & Martorell, S., 2023. "Prognosis of wear-out effect on of safety equipment reliability for nuclear power plants long-term safe operation," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    5. 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).
    6. Meng, Yuan & Zhang, Dequan & Shi, Baojun & Wang, Dapeng & Wang, Fang, 2024. "An active learning Kriging model with approximating parallel strategy for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    7. Yu, Shui & Ren, Yuyao & Wu, Xiao & Guo, Peng & Li, Yun, 2024. "Dynamic pruning-based Bayesian support vector regression for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    8. Wang, Bo & Jiang, Ping & Guo, Bo, 2024. "A Bayesian design method for monopropellant engine system reliability qualification test plan," Reliability Engineering and System Safety, Elsevier, vol. 248(C).

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