Heterogeneous Degradation Modeling Based on Hierarchical Bayesian Model and Wiener Process

In this paper, a hierarchical Bayesian model is presented with heterogeneous degradation data populations based on Wiener process and Gaussian mixture model, where the actual degradation path is described by Wiener process, and the Gaussian mixture model is used to capture the heterogeneity between data populations. The Bayesian parameters estimation method is carried out via hierarchical priors and Gibbs sampling algorithm, and DIC and WAIC are the two selection criteria for the optimal model to fit the data. A set of GaAs laser numerical example indicates that the heterogeneous degradation data population with two sub-populations provides a better reliability assessment result than assuming a homogeneous population.