Meta-analysis of a step-stress experiment under Weibull distribution

In this article, we mainly focus on the meta-analysis of several simple step-stress experimental data sets. It is assumed that independent data sets are obtained from s simple step-stress experiments. It is further assumed that the lifetime of the experimental units follow two parameter Weibull distribution with different shape and scale parameters at different stress levels. The classical and Bayesian inference of the model parameters have been provided. Since the closed-form solution of maximum-likelihood estimators of the model parameters do not exist, asymptotic properties of the estimators have been used to construct confidence intervals. On the other hand, Gibbs sampling technique has been used to obtain the Bayes estimates and the associated credible intervals of the model parameters. Extensive simulation experiments have been performed to assess the performance of the proposed methods, and the analyses of two data sets have been presented for illustrative purpose.