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A discretization procedure for rare events in Bayesian networks

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  • Zwirglmaier, Kilian
  • Straub, Daniel

Abstract

Discrete Bayesian networks (BNs) can be effective for risk- and reliability assessments, in which probability estimates of (rare) failure events are frequently updated with new information. To solve such reliability problems accurately in BNs, the discretization of continuous random variables must be performed carefully. To this end, we develop an efficient discretization scheme, which is based on finding an optimal discretization for the linear approximation of the reliability problem obtained from the First-Order Reliability Method (FORM). Because the probability estimate should be accurate under all possible future information scenarios, the discretization scheme is optimized with respected to the expected posterior error. To simplify application of the method, we establish parametric formulations for efficient discretization of random variables in BNs for reliability problems based on numerical investigations. The procedure is implemented into a software prototype. Finally, it is applied to a verification example and an application example, the prediction of runway overrun of a landing aircraft.

Suggested Citation

  • Zwirglmaier, Kilian & Straub, Daniel, 2016. "A discretization procedure for rare events in Bayesian networks," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 96-109.
    • Handle: RePEc:eee:reensy:v:153:y:2016:i:c:p:96-109
    DOI: 10.1016/j.ress.2016.04.008
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    References listed on IDEAS

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    1. Langseth, Helge & Nielsen, Thomas D. & Rumí, Rafael & Salmerón, Antonio, 2009. "Inference in hybrid Bayesian networks," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1499-1509.
    2. Neil, Martin & Tailor, Manesh & Marquez, David & Fenton, Norman & Hearty, Peter, 2008. "Modelling dependable systems using hybrid Bayesian networks," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 933-939.
    3. Zhu, Jiandao & Collette, Matthew, 2015. "A dynamic discretization method for reliability inference in Dynamic Bayesian Networks," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 242-252.
    4. Hanea, Anca & Morales Napoles, Oswaldo & Ababei, Dan, 2015. "Non-parametric Bayesian networks: Improving theory and reviewing applications," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 265-284.
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    Cited by:

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    2. Tosoni, E. & Salo, A. & Govaerts, J. & Zio, E., 2019. "Comprehensiveness of scenarios in the safety assessment of nuclear waste repositories," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 561-573.
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    4. Lee, Dooyoul & Kwon, Kybeom, 2023. "Dynamic Bayesian network model for comprehensive risk analysis of fatigue-critical structural details," Reliability Engineering and System Safety, Elsevier, vol. 229(C).

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