Bayesian analysis of constant-stress accelerated life test for the Weibull distribution using noninformative priors

Abstract Noninformative priors are used in estimating the model parameters in constant-stress accelerated life tests (ALTs) under Type-II censoring when the Weibull distributions are assumed. Several reference priors and the general forms of the probability matching priors are derived. It is verified that one of the reference priors is the unique second-order jointly probability matching prior. The propriety of the posteriors based on the reference priors is shown. It shows that the matching prior performs better than the other two reference priors in meeting the target coverage probabilities. A real data set from Nelson (1990) is analyzed for illustration.

[1]  T. Fan,et al.  Constant Stress Accelerated Life Test on a Multiple-Component Series System under Weibull Lifetime Distributions , 2014 .

[2]  Chiranjit Mukhopadhyay,et al.  Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure , 2014 .

[3]  G. Datta.  On priors providing frequentist validity of Bayesian inference for multiple parametric functions , 1996 .

[4]  Yincai Tang,et al.  Objective Bayesian analysis of accelerated competing failure models under Type-I censoring , 2011, Comput. Stat. Data Anal..

[5]  Jürgen Pilz,et al.  Applying Bayesian mixtures-of-experts models to statistical description of smart power semiconductor reliability , 2011, Microelectron. Reliab..

[6]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[7]  H. W. Peers.  On Confidence Points and Bayesian Probability Points in the Case of Several Parameters , 1965 .

[8]  Trevor J. Sweeting,et al.  Probability matching priors , 2004 .

[9]  S. Voiculescu,et al.  Bayesian estimation in accelerated life testing application on exponential-arrhenius model , 2006, RAMS '06. Annual Reliability and Maintainability Symposium, 2006..

[10]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[11]  Sorin Voiculescu,et al.  Pseudo-conjugated prior distribution for parametric ALT model , 2011, 2011 Proceedings - Annual Reliability and Maintainability Symposium.

[12]  W. Meeker.  Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[13]  Keming Yu,et al.  New Inference for Constant-Stress Accelerated Life Tests With Weibull Distribution and Progressively Type-II Censoring , 2014, IEEE Transactions on Reliability.

[14]  Mihaela Barreau,et al.  Bayesian estimation in accelerated life testing , 2009 .

[15]  D. Dey,et al.  Frequentist validity of posterior quantiles in the presence of a nuisance parameter : higher order asymptotics , 1993 .

[16]  Michel Loève,et al.  Probability Theory I , 1977 .

[17]  A. F. Attia,et al.  Estimation in Constant-Stress Accelerated Life Testing for Birnbaum-Saunders Distribution under Censoring , 2013 .