Bayesian optimal design of step stress accelerated degradation testing

Abstract

This study presents a Bayesian methodology for designing step stress accelerated degradation testing (SSADT) and its application to batteries. First, the simulation-based Bayesian design framework for SSADT is presented. Then, by considering historical data, specific optimal objectives oriented Kullback-Leibler (KL) divergence is established. A numerical example is discussed to illustrate the design approach. It is assumed that the degradation model (or process) follows a drift Brownian motion; the acceleration model follows Arrhenius equation; and the corresponding parameters follow normal and Gamma prior distributions. Using the Markov Chain Monte Carlo (MCMC) method and WinBUGS software, the comparison shows that KL divergence is better than quadratic loss for optimal criteria. Further, the effect of simulation outliers on the optimization plan is analyzed and the preferred surface fitting algorithm is chosen. At the end of the paper, a NASA lithium-ion battery dataset is used as historical information and the KL divergence oriented Bayesian design is compared with maximum likelihood theory oriented locally optimal design. The results show that the proposed method can provide a much better testing plan for this engineering application.