A Complete Bayesian Degradation Analysis Based on Inverse Gaussian Processes

Degradation models are constructed for the observations of a quality characteristic related to the failure time of products. The failure time inference of the product is derived based on the first passage time to a specific threshold for the selected degradation model. The Bayesian analysis incorporated with valuable prior information from expert opinion or experience is a helpful approach, in particular for small sample sizes. However, most Bayesian research focuses more on the degradation model than the failure time inference. This study uses Bayesian predictive analysis based on the inverse Gaussian process with conjugate priors to deduce the failure time inference. The posterior inference of the parameters for the fixed-effect linear degradation model is derived in closed forms, and the full conditional posteriors are developed for the random-effect models using hierarchical modeling. The failure time inference associated with the degradation model and its goodness-of-fit test is suggested from a complete Bayesian perspective. The proposed failure time inference can be used for other degradation models with random effect. Two illustrative examples demonstrate the feasibility and advantages of the proposed Bayesian approach.