In this study, we develop a hierarchical Bayesian GLFP framework based on log-normal lifetime distributions to accommodate population heterogeneity. By introducing latent variables through data augmentation, the complete likelihood exhibits conjugacy, enabling a more efficient Markov chain Monte Carlo (MCMC) procedure. The posterior samples of the latent variables naturally allow predictions of failure modes and defect status for individual devices. An application to a subset of hard-drive failure data from the Backblaze company, hopefully, can further illustrate the practicality and feasibility of the proposed method.
