Inference for step-stress plan with Khamis-Higgins model under type-II censored Weibull data

The accelerated life testing (ALT) is frequently used in examining the component reliability and acceptance testing. The ALT is carried out by exposing the unit to higher stress levels in order to observe data faster than those are producing under the normal conditions. The simple step-stress model based on type-II censoring Weibull lifetimes is studied here. In addition, the lifetimes satisfy Khamis-Higgins model assumption. In this paper, Bayesian approaches are developed for estimating the model parameters and predicting times to failure of future censored of the simple step-stress model from Weibull distribution using Khamis-Higgins model. The main goal of this work consists of two parts. First, the Bayesian estimation of the unknown parameters involved in the model is considered by adopting Devroye method to generate log-concave densities within sampling-based algorithm under different loss functions. The Bayes and highest posterior density credible intervals are then established. Second, the estimation of the posterior predictive density of the future lifetimes are discussed to obtain the point and prediction intervals with a given coverage probability. Monte Carlo simulation is performed to check the efficiency of the developed procedures and analyze a real data set for illustrative purposes.