IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v94y2009i2p463-473.html
   My bibliography  Save this article

Bayesian estimation of mixed Weibull distributions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832008001555
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2008.05.004?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

    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:eee:reensy:v:94:y:2009:i:2:p:463-473. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.