Bayesian inference for the simple step-stress accelerated life tests under order-restriction

Abstract

In this work, we investigate the order-restricted Bayesian estimation for a simple step-stress accelerated life tests. Based on the three-parameter gamma distribution as a conditional prior, we ensure that the failure rates increase as the stress level increases. In addition, its conjugate-like structure enables us to derive the exact joint posterior distribution of the parameters without a need to perform an expensive MCMC sampling. Upon these distributional results, several Bayesian estimators for the model parameters are suggested along with their individual/joint credible intervals. Through Monte Carlo simulations, the performance of our proposed inferential methods are assessed and compared. Finally, a real engineering case study for analyzing the reliability of a solar lighting device is presented to illustrate the methods developed in this work.