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Formulating informative, data-based priors for failure probability estimation in reliability analysis

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  • Guikema, Seth D.

Abstract

Priors play an important role in the use of Bayesian methods in risk analysis, and using all available information to formulate an informative prior can lead to more accurate posterior inferences. This paper examines the practical implications of using five different methods for formulating an informative prior for a failure probability based on past data. These methods are the method of moments, maximum likelihood (ML) estimation, maximum entropy estimation, starting from a non-informative ‘pre-prior’, and fitting a prior based on confidence/credible interval matching. The priors resulting from the use of these different methods are compared qualitatively, and the posteriors are compared quantitatively based on a number of different scenarios of observed data used to update the priors. The results show that the amount of information assumed in the prior makes a critical difference in the accuracy of the posterior inferences. For situations in which the data used to formulate the informative prior is an accurate reflection of the data that is later observed, the ML approach yields the minimum variance posterior. However, the maximum entropy approach is more robust to differences between the data used to formulate the prior and the observed data because it maximizes the uncertainty in the prior subject to the constraints imposed by the past data.

Suggested Citation

  • Guikema, Seth D., 2007. "Formulating informative, data-based priors for failure probability estimation in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 490-502.
  • Handle: RePEc:eee:reensy:v:92:y:2007:i:4:p:490-502
    DOI: 10.1016/j.ress.2006.01.002
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    1. Carl S. Spetzler & Carl-Axel S. Staël Von Holstein, 1975. "Exceptional Paper--Probability Encoding in Decision Analysis," Management Science, INFORMS, vol. 22(3), pages 340-358, November.
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    Cited by:

    1. Song, Cen & Zhuang, Jun, 2017. "N-stage security screening strategies in the face of strategic applicants," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 292-301.
    2. Seth D. Guikema & Jeremy P. Goffelt, 2008. "A Flexible Count Data Regression Model for Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 28(1), pages 213-223, February.
    3. Roger Zoh & Alyson Wilson & Scott Vander Wiel & Earl Lawrence, 2018. "The negative log-gamma prior distribution for Bayesian assessment of system reliability," Journal of Risk and Reliability, , vol. 232(3), pages 308-319, June.
    4. Yingchun Xu & Xiaohu Zheng & Wen Yao & Ning Wang & Xiaoqian Chen, 2021. "A sequential multi-prior integration and updating method for complex multi-level system based on Bayesian melding method," Journal of Risk and Reliability, , vol. 235(5), pages 863-876, October.
    5. Eryilmaz, Serkan, 2011. "Estimation in coherent reliability systems through copulas," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 564-568.

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