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Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis

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  • Simon, C.
  • Weber, P.
  • Evsukoff, A.

Abstract

This paper deals with the use of Bayesian networks to compute system reliability. The reliability analysis problem is described and the usual methods for quantitative reliability analysis are presented within a case study. Some drawbacks that justify the use of Bayesian networks are identified. The basic concepts of the Bayesian networks application to reliability analysis are introduced and a model to compute the reliability for the case study is presented. Dempster Shafer theory to treat epistemic uncertainty in reliability analysis is then discussed and its basic concepts that can be applied thanks to the Bayesian network inference algorithm are introduced. Finally, it is shown, with a numerical example, how Bayesian networks’ inference algorithms compute complex system reliability and what the Dempster Shafer theory can provide to reliability analysis.

Suggested Citation

  • Simon, C. & Weber, P. & Evsukoff, A., 2008. "Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 950-963.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:7:p:950-963
    DOI: 10.1016/j.ress.2007.03.012
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    References listed on IDEAS

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    3. P. Walley & S. Moral, 1999. "Upper probabilities based only on the likelihood function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 831-847.
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    Citations

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    1. C Simon & P Weber, 2009. "Imprecise reliability by evidential networks," Journal of Risk and Reliability, , vol. 223(2), pages 119-131, June.
    2. Yu, Yaocheng & Shuai, Bin & Huang, Wencheng, 2024. "Resilience evaluation of train control on-board system considering common cause failure: Based on a beta-factor and continuous-time bayesian network model," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    3. González, Esteban Le Maitre & Desforges, Xavier & Archimède, Bernard, 2018. "Assessment method of the multicomponent systems future ability to achieve productive tasks from local prognoses," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 403-415.
    4. Mi, Jinhua & Li, Yan-Feng & Peng, Weiwen & Huang, Hong-Zhong, 2018. "Reliability analysis of complex multi-state system with common cause failure based on evidential networks," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 71-81.
    5. El Hassene Ait Mokhtar & Radouane Laggoune & Alaa Chateauneuf, 2016. "Utility-Based Maintenance Optimization for Complex Water-Distribution Systems Using Bayesian Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(12), pages 4153-4170, September.
    6. Weidong Zhu & Shaorong Li & Hongtao Zhang & Tianjiao Zhang & Zhimin Li, 2022. "Evaluation of scientific research projects on the basis of evidential reasoning approach under the perspective of expert reliability," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(1), pages 275-298, January.
    7. Simon, Christophe & Bicking, Frédérique, 2017. "Hybrid computation of uncertainty in reliability analysis with p-box and evidential networks," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 629-638.
    8. Ait Mokhtar, El Hassene & Laggoune, Radouane & Chateauneuf, Alaa, 2023. "Imperfect maintenance modeling and assessment of repairable multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    9. Felipe Aguirre & Mohamed Sallak & Walter Schön & Fabien Belmonte, 2013. "Application of evidential networks in quantitative analysis of railway accidents," Journal of Risk and Reliability, , vol. 227(4), pages 368-384, August.
    10. Liu, Qiang, 2021. "Reliability evaluation of two-stage evidence classification system considering preference and error," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    11. Limbourg, Philipp & de Rocquigny, Etienne, 2010. "Uncertainty analysis using evidence theory – confronting level-1 and level-2 approaches with data availability and computational constraints," Reliability Engineering and System Safety, Elsevier, vol. 95(5), pages 550-564.
    12. El Hassene Ait Mokhtar & Radouane Laggoune & Alaa Chateauneuf, 2017. "Benefit and customer demand approach for maintenance optimization of complex systems using Bayesian networks," Journal of Risk and Reliability, , vol. 231(5), pages 558-572, October.
    13. Yu, Yaocheng & Shuai, Bin & Huang, Wencheng, 2024. "Resilience evaluation of train control on-board system based on multi-dimensional continuous-time Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    14. Mi, Jinhua & Lu, Ning & Li, Yan-Feng & Huang, Hong-Zhong & Bai, Libing, 2022. "An evidential network-based hierarchical method for system reliability analysis with common cause failures and mixed uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    15. Zhang, Xiaoge & Mahadevan, Sankaran & Deng, Xinyang, 2017. "Reliability analysis with linguistic data: An evidential network approach," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 111-121.
    16. Radim Briš & Petr Byczanski, 2017. "On innovative stochastic renewal process models for exact unavailability quantification of highly reliable systems," Journal of Risk and Reliability, , vol. 231(6), pages 617-627, December.

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