A Hierarchical Bayesian Degradation Model for Heterogeneous Data

Degradation data may be collected from a population with heterogeneous subpopulations. This paper contributes to the development of a new statistical modeling and computation method for analyzing heterogeneous degradation data. We adopt the random-coefficient degradation path approach, and propose a hierarchical Bayesian degradation model. To account for the heterogeneity, we model the unit-to-unit variability via random parameters in a Gaussian mixture model. We developed a computationally convenient algorithm that combines Gibbs sampling for parameter estimation as well as failure-time distribution prediction and Akaike information criterion for determining the number of subpopulations. A numerical example is used to illustrate the advantages of the proposed methodology over existing methods that do not explicitly consider heterogeneity in the degradation data.