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Objective Bayesian analysis of accelerated competing failure models under Type-I censoring

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  • Xu, Ancha
  • Tang, Yincai

Abstract

This paper discusses the Bayesian inference of accelerated life tests (ALT) in the presence of competing failure causes. The time to failure due to a specific cause is described by a Weibull distribution. A two-stage approach is utilized to obtain the estimates of parameters in the model. We use the Bayesian method to estimate the parameters of the distribution of component lifetimes in the first stage, in which two noninformative priors (Jeffreys prior and reference prior) are derived in the case of ALT, and based on these two priors we present the Gibbs sampling procedures to obtain the posterior estimates of the parameters. Besides, to overcome the problem of improper posterior densities under some conditions, we modify the likelihood function to make the posterior densities proper. In the second stage, parameters in the accelerating function are obtained by least squares approach. A numerical example is given to show the effectiveness of the method and a real data from Nelson (1990) is analyzed.

Suggested Citation

  • Xu, Ancha & Tang, Yincai, 2011. "Objective Bayesian analysis of accelerated competing failure models under Type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2830-2839, October.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:10:p:2830-2839
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    References listed on IDEAS

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    1. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
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    Cited by:

    1. Herbert Hove & Frank Beichelt & Parmod K. Kapur, 2017. "Estimation of the Frank copula model for dependent competing risks in accelerated life testing," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 673-682, December.
    2. Liudong Xing & Chaonan Wang & Gregory Levitin, 2012. "Competing failure analysis in non-repairable binary systems subject to functional dependence," Journal of Risk and Reliability, , vol. 226(4), pages 406-416, August.
    3. Kazianka, Hannes, 2012. "Objective Bayesian analysis for the normal compositional model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1528-1544.
    4. Guan, Qiang & Tang, Yincai & Xu, Ancha, 2013. "Objective Bayesian analysis for bivariate Marshall–Olkin exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 299-313.

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