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Bayesian Estimation of Life Parameters in the Weibull Distribution

Author

Listed:
  • George C. Canavos

    (NASA Langley Research Center, Hampton Virginia)

  • Chris P. Taokas

    (University of South Florida, Tampa, Florida)

Abstract

This paper develops a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter θ, Bayesian estimates of θ and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results [ J. Am. Stat. Assn. 62, 48–62 (1967)] for the one-parameter exponential life-testing distribution are reduced to a special case of these results. The paper develops a fully Bayesian analysis of both the scale and shape parameters θ and ξ by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of a Monte Carlo simulation and numerical-integration techniques. In both cases, the paper carries out a computer simulation and makes a comparison between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:3:p:755-763
    DOI: 10.1287/opre.21.3.755
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    Cited by:

    1. de Jonge, Bram & Dijkstra, Arjan S. & Romeijnders, Ward, 2015. "Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 15-21.
    2. Hassan M. Okasha & Heba S. Mohammed & Yuhlong Lio, 2021. "E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications," Mathematics, MDPI, vol. 9(11), pages 1-19, May.
    3. Zhou, Chongwen & Chinnam, Ratna Babu & Dalkiran, Evrim & Korostelev, Alexander, 2017. "Bayesian approach to hazard rate models for early detection of warranty and reliability problems using upstream supply chain information," International Journal of Production Economics, Elsevier, vol. 193(C), pages 316-331.
    4. Touw, Anduin E., 2009. "Bayesian estimation of mixed Weibull distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 463-473.
    5. Hryniewicz, Olgierd, 2016. "Bayes statistical decisions with random fuzzy data—an application in reliability," Reliability Engineering and System Safety, Elsevier, vol. 151(C), pages 20-33.
    6. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    7. de Jonge, Bram & Klingenberg, Warse & Teunter, Ruud & Tinga, Tiedo, 2015. "Optimum maintenance strategy under uncertainty in the lifetime distribution," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 59-67.

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