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Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data

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  • Soliman, Ahmed A.
  • Abd-Ellah, Ahmed H.
  • Abou-Elheggag, Naser A.
  • Ahmed, Essam A.

Abstract

In this paper, we investigate the problem of point and interval estimations for the modified Weibull distribution (MWD) using progressively type-II censored sample. The maximum likelihood (ML), Bayes, and parametric bootstrap methods are used for estimating the unknown parameters as well as some lifetime parameters (reliability and hazard functions). Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. Bayes estimates and the credible intervals are obtained under the assumptions of informative and noninformative priors. The results of Bayes method are obtained under both the balanced squared error loss (bSEL) and balanced linear-exponential (bLINEX) loss. We show that these loss functions are more general, which include the MLE and both symmetric and asymmetric Bayes estimates as special cases. Finally, Two real data sets have been analyzed for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:100:y:2012:i:c:p:48-57
    DOI: 10.1016/j.ress.2011.12.013
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    References listed on IDEAS

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    Cited by:

    1. Tien Thanh Thach & Radim Bris, 2020. "Improved new modified Weibull distribution: A Bayes study using Hamiltonian Monte Carlo simulation," Journal of Risk and Reliability, , vol. 234(3), pages 496-511, June.
    2. Almalki, Saad J. & Yuan, Jingsong, 2013. "A new modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 164-170.
    3. Abba, Badamasi & Wang, Hong & Bakouch, Hassan S., 2022. "A reliability and survival model for one and two failure modes system with applications to complete and censored datasets," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    4. Shuto, Susumu & Amemiya, Takashi, 2022. "Sequential Bayesian inference for Weibull distribution parameters with initial hyperparameter optimization for system reliability estimation," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    5. Ziyad A. Alhussain & Essam A. Ahmed, 2020. "Estimation of exponentiated Nadarajah-Haghighi distribution under progressively type-II censored sample with application to bladder cancer data," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 631-657, June.
    6. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
    7. Chemweno, Peter & Pintelon, Liliane & Muchiri, Peter Nganga & Van Horenbeek, Adriaan, 2018. "Risk assessment methodologies in maintenance decision making: A review of dependability modelling approaches," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 64-77.
    8. Zhao, Yan-Gang & Zhang, Xuan-Yi & Lu, Zhao-Hui, 2018. "A flexible distribution and its application in reliability engineering," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 1-12.

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