Bayesian accelerated life testing models for the log-normal and gamma distributions under dual-stresses

Abstract

In this paper, a Bayesian approach to accelerated life testing models with two stressors is presented. Lifetimes are assumed to follow either a log-normal distribution or a gamma distribution, which have been mostly overlooked in the Bayesian literature when considering multiple stressors. The generalized Eyring relationship is used as the time transformation function, which allows for the use of one thermal stressor and one non-thermal stressor. Due to the mathematically intractable posteriors of these models, Markov chain Monte Carlo methods are utilized to obtain posterior samples on which to base inference. The models are applied to a real dataset, where model comparison metrics are calculated and estimates are provided of the model parameters, predictive reliability, and mean time to failure. The robustness of the models is also investigated in terms of the prior specification.