IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v21y1973i3p755-763.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.21.3.755
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.21.3.755?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Touw, Anduin E., 2009. "Bayesian estimation of mixed Weibull distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 463-473.
    7. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:21:y:1973:i:3:p:755-763. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.