Bayesian Analysis of a Simple Step-Stress Model Under Weibull Lifetimes

The step-stress model is becoming quite popular for analyzing lifetime data obtained from accelerated life testing experiments. In the usual step-stress experiment, stress levels are allowed to change at each step to get rapid failure of the experimental units. The simple step-stress model under different censoring schemes based on Weibull lifetimes is considered in this paper. It is assumed that the lifetime distributions of the experimental units have different scale parameters at different stress levels, but they have the same shape parameter. Moreover, it is assumed that the lifetimes follow the Khamis-Higgins model. It is further assumed that, as the stress level increases, the scale parameter also increases. We provide Bayesian inference of the unknown parameters of the Weibull distribution under this order restriction on the scale parameters. Monte Carlo simulations have been performed to see the effectiveness of the proposed method, and a data set has been analyzed for illustrative purposes.