Objective Bayesian Analysis for Step-Stress Accelerated Degradation Test Based on Wiener Process Models

Step-stress accelerated degradation test (SSADT) is a useful tool for assessing the lifetime distribution of highly reliable products when the available test items are very few. In this paper, we discuss multiple-steps step-stress accelerated degradation models based on Wiener process, and we apply the objective Bayesian method for such analytically intractable models to obtain the noninformative priors (Jefferys prior and two Reference priors). Moreover, we show that their posterior distributions are proper, and we propose Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two Reference priors. Finally, we present some simulation studies to compare the objective Bayesian estimates with the other Bayesian estimate and the maximum likelihood estimates (MLEs). Simulation results demonstrate the superiority of objective Bayesian analysis method.