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A Bayesian Monte Carlo-based algorithm for the estimation of small failure probabilities of systems affected by uncertainties

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  • Cadini, F.
  • Gioletta, A.

Abstract

The estimation of system failure probabilities in presence of uncertainties may be a difficult task when the values involved are very small, so that sampling-based Monte Carlo methods may become computationally impractical, especially if the computer codes used to model the system response require large computational efforts, both in terms of time and memory. In this work, we propose to exploit the Bayesian Monte Carlo (BMC) approach to the estimation of definite integrals for developing a new, efficient algorithm for estimating small failure probabilities. The Bayesian framework allows an effective use of all the information available, i.e. the computer code evaluations and the input uncertainty distributions, and, at the same time, the analytical formulation of the Bayesian estimator guarantees the construction of a computationally lean algorithm. The proposed method is first satisfactorily tested with reference to an analytic, two-dimensional case study of literature, offering satisfactory results; then, it is applied to a realistic case study of a natural convection-based cooling system of a gas-cooled fast reactor, operating under a post-loss-of-coolant accident (LOCA), showing performances comparable to those of other efficient alternative methods of literature.

Suggested Citation

  • Cadini, F. & Gioletta, A., 2016. "A Bayesian Monte Carlo-based algorithm for the estimation of small failure probabilities of systems affected by uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 15-27.
  • Handle: RePEc:eee:reensy:v:153:y:2016:i:c:p:15-27
    DOI: 10.1016/j.ress.2016.04.003
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    References listed on IDEAS

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    1. Cadini, F. & Santos, F. & Zio, E., 2014. "An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 109-117.
    2. Echard, B. & Gayton, N. & Lemaire, M. & Relun, N., 2013. "A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 232-240.
    3. Cadini, F. & Gioletta, A. & Zio, E., 2015. "Improved metamodel-based importance sampling for the performance assessment of radioactive waste repositories," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 188-197.
    4. Enrico Zio, 2013. "System Reliability and Risk Analysis," Springer Series in Reliability Engineering, in: The Monte Carlo Simulation Method for System Reliability and Risk Analysis, edition 127, chapter 0, pages 7-17, Springer.
    5. Enrico Zio, 2013. "Monte Carlo Simulation: The Method," Springer Series in Reliability Engineering, in: The Monte Carlo Simulation Method for System Reliability and Risk Analysis, edition 127, chapter 0, pages 19-58, Springer.
    6. Enrico Zio, 2013. "The Monte Carlo Simulation Method for System Reliability and Risk Analysis," Springer Series in Reliability Engineering, Springer, edition 127, number 978-1-4471-4588-2, March.
    7. Enrico Zio, 2013. "System Reliability and Risk Analysis by Monte Carlo Simulation," Springer Series in Reliability Engineering, in: The Monte Carlo Simulation Method for System Reliability and Risk Analysis, edition 127, chapter 0, pages 59-81, Springer.
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    Cited by:

    1. Bansal, Sahil & Cheung, Sai Hung, 2017. "On the evaluation of multiple failure probability curves in reliability analysis with multiple performance functions," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 583-594.
    2. Cheng, Kai & Lu, Zhenzhou, 2021. "Adaptive Bayesian support vector regression model for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 206(C).
    3. Da Hye Lee & In Hong Chang & Hoang Pham, 2020. "Software Reliability Model with Dependent Failures and SPRT," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    4. Bansal, Sahil & Cheung, Sai Hung, 2018. "A subset simulation based approach with modified conditional sampling and estimator for loss exceedance curve computation," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 94-107.
    5. Menz, Morgane & Gogu, Christian & Dubreuil, Sylvain & Bartoli, Nathalie & Morio, Jérôme, 2020. "Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    6. Shang, Xiaobing & Su, Li & Fang, Hai & Zeng, Bowen & Zhang, Zhi, 2023. "An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    7. Cheng, Kai & Lu, Zhenzhou, 2019. "Time-variant reliability analysis based on high dimensional model representation," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 310-319.
    8. Cadini, Francesco & Agliardi, Gian Luca & Zio, Enrico, 2017. "Estimation of rare event probabilities in power transmission networks subject to cascading failures," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 9-20.
    9. Zywiec, William J. & Mazzuchi, Thomas A. & Sarkani, Shahram, 2021. "Analysis of process criticality accident risk using a metamodel-driven Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

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