Inference of multi‐sample stage life testing model under Weibull distribution

Abstract

In this article we consider the meta‐analysis of stage life testing experiments. We propose a method to combine the data obtained from number of independent stage life testing experiments. We have assumed that there are only two stress levels for each stage life testing experiment and lifetime of the experimental units follows Weibull distribution at each stress level. The distributions under two stress levels are connected through Khamis–Higgings model assumption. We assume that the shape parameters of Weibull distribution are same for all the samples; however, the scale parameters are different. We provide the maximum likelihood estimation and the asymptotic confidence intervals of the model parameters. We also provide the Bayesian inference of the model parameters. The Bayes estimates and the associated credible intervals are obtained using Gibbs sampling technique since the explicit forms of the Bayes estimates do not exist. We have performed an extensive simulation study to see the performances of the different estimators, and the analyses of two data sets for illustrative purpose. The results are quite satisfactory.