Semi-parametric Bayesian models for heterogeneous degradation data: An application to laser data

Abstract

Degradation data are considered to make reliability assessments in highly reliable systems. The class of general path models is a popular tool to approach degradation data. In this class of models, the random effects represent the correlations between degradation measures. Random effects are interpreted in terms of the degradation rates, which facilitates the specification of their prior distribution. The usual approaches assume that degradation comes from a homogeneous population. This assumption is strong, mainly, if the variability in the manufacturing process is high or if there are no guarantees that the devices work on similar conditions. To account for heterogeneous degradation data, we develop semi-parametric degradation models based on the Dirichlet process mixture of both, normal and skew-normal distributions. The proposed model also describes skewness and heavy-tail behavior in degradation data. We prove that the proposed model also accounts for heterogeneity in the lifetime data. We propose a method to build the prior distributions adapting previous approaches to the context in which mixture models fit latent variables. We carry out simulation studies and data analysis to show the flexibility of the proposed model in modeling skewness, heavy tail and multi-modal behavior of the random effects.