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Evaluation and comparison of estimation methods for failure rates and probabilities

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  • Vaurio, Jussi K.
  • Jänkälä, Kalle E.

Abstract

An updated parametric robust empirical Bayes (PREB) estimation methodology is presented as an alternative to several two-stage Bayesian methods used to assimilate failure data from multiple units or plants. PREB is based on prior-moment matching and avoids multi-dimensional numerical integrations. The PREB method is presented for failure-truncated and time-truncated data. Erlangian and Poisson likelihoods with gamma prior are used for failure rate estimation, and Binomial data with beta prior are used for failure probability per demand estimation. Combined models and assessment uncertainties are accounted for. One objective is to compare several methods with numerical examples and show that PREB works as well if not better than the alternative more complex methods, especially in demanding problems of small samples, identical data and zero failures. False claims and misconceptions are straightened out, and practical applications in risk studies are presented.

Suggested Citation

  • Vaurio, Jussi K. & Jänkälä, Kalle E., 2006. "Evaluation and comparison of estimation methods for failure rates and probabilities," Reliability Engineering and System Safety, Elsevier, vol. 91(2), pages 209-221.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:2:p:209-221
    DOI: 10.1016/j.ress.2005.01.001
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    References listed on IDEAS

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    1. Eduard Hofer & Stephen C. Hora & Ronald L. Iman & Jörg Peschke, 1997. "On the Solution Approach for Bayesian Modeling of Initiating Event Frequencies and Failure Rates," Risk Analysis, John Wiley & Sons, vol. 17(2), pages 249-252, April.
    2. Jussi K. Vaurio, 1994. "Estimation of Common Cause Failure Rates Based on Uncertain Event Data," Risk Analysis, John Wiley & Sons, vol. 14(4), pages 383-387, August.
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    Cited by:

    1. Chen, Qian & Zuo, Lili & Wu, Changchun & Li, Yun & Hua, Kaixun & Mehrtash, Mahdi & Cao, Yankai, 2022. "Optimization of compressor standby schemes for gas transmission pipeline systems based on gas delivery reliability," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    2. Diaz, Juan Esteban & Handl, Julia & Xu, Dong-Ling, 2018. "Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system," European Journal of Operational Research, Elsevier, vol. 266(3), pages 976-989.
    3. Quigley, John & Bedford, Tim & Walls, Lesley, 2007. "Estimating rate of occurrence of rare events with empirical bayes: A railway application," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 619-627.
    4. Strigini, Lorenzo & Wright, David, 2014. "Bounds on survival probability given mean probability of failure per demand; and the paradoxical advantages of uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 66-83.
    5. Zhao, Xingyu & Littlewood, Bev & Povyakalo, Andrey & Strigini, Lorenzo & Wright, David, 2018. "Conservative claims for the probability of perfection of a software-based system using operational experience of previous similar systems," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 265-282.
    6. Hu, Shenping & Fang, Quangen & Xia, Haibo & Xi, Yongtao, 2007. "Formal safety assessment based on relative risks model in ship navigation," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 369-377.
    7. Viertävä, Janne & Vaurio, Jussi K., 2009. "Testing statistical significance of trends in learning, ageing and safety indicators," Reliability Engineering and System Safety, Elsevier, vol. 94(6), pages 1128-1132.
    8. Quigley, John & Hardman, Gavin & Bedford, Tim & Walls, Lesley, 2011. "Merging expert and empirical data for rare event frequency estimation: Pool homogenisation for empirical Bayes models," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 687-695.
    9. Quigley, John & Walls, Lesley, 2011. "Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 933-941.

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