Inference for multi-sample stage life testing under the inverse Weibull distribution with a Khamis–Higgins link

Abstract

Abstract This article develops a methodology for the meta-analysis of stage life testing experiments, combining data from s independent tests. Each experiment involves two stress levels, with the lifetime of experimental units at each level following an inverse Weibull distribution. The Khamis–Higgins model is used to relate the distributions across the two stress levels. The shape parameter of the inverse Weibull distribution is assumed constant across all samples, while the scale parameters are allowed to vary. We derive maximum likelihood estimators and asymptotic confidence intervals for the model parameters. Bayesian inference is also conducted; due to the lack of closed-form posterior expressions, Bayes estimates and credible intervals are obtained via Gibbs sampling. An extensive simulation study evaluates the performance of the proposed estimators, and two real datasets are analyzed for illustration. The findings collectively demonstrate the effectiveness of the proposed methodology.