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Bayesian estimation of mixed Weibull distributions

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  • Touw, Anduin E.

Abstract

Estimation of mixed Weibull distribution by maximum likelihood estimation and other methods is frequently difficult due to unstable estimates arising from limited data. Bayesian techniques can stabilize these estimates through the priors, but there is no closed-form conjugate family for the Weibull distribution. This paper reduces the number of numeric integrations required for using Bayesian estimation on mixed Weibull situations from five to two, thus making it a more feasible approach to the typical user. It also examines the robustness of the Bayesian estimates under a variety of different prior distributions. It is found that Bayesian estimation can improve accuracy over the MLE for situations with low mixture ratios so long as the prior on the weak subpopulation's characteristic life has an expected value less than or equal to the true characteristic life.

Suggested Citation

  • Touw, Anduin E., 2009. "Bayesian estimation of mixed Weibull distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 463-473.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:2:p:463-473
    DOI: 10.1016/j.ress.2008.05.004
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    References listed on IDEAS

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    1. George C. Canavos & Chris P. Taokas, 1973. "Bayesian Estimation of Life Parameters in the Weibull Distribution," Operations Research, INFORMS, vol. 21(3), pages 755-763, June.
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    Cited by:

    1. Soliman, Ahmed A. & Abd-Ellah, Ahmed H. & Abou-Elheggag, Naser A. & Ahmed, Essam A., 2012. "Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 48-57.
    2. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.
    3. Wang, Lizhi & Pan, Rong & Li, Xiaoyang & Jiang, Tongmin, 2013. "A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 38-47.
    4. Goh, H.H. & Lee, S.W. & Chua, Q.S. & Goh, K.C. & Teo, K.T.K., 2016. "Wind energy assessment considering wind speed correlation in Malaysia," Renewable and Sustainable Energy Reviews, Elsevier, vol. 54(C), pages 1389-1400.
    5. Wang, Lizhi & Pan, Rong & Wang, Xiaohong & Fan, Wenhui & Xuan, Jinquan, 2017. "A Bayesian reliability evaluation method with different types of data from multiple sources," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 128-135.

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