Bayesian Analysis for Lifetime Delayed Degradation Process

Abstract

The Lifetime Delayed Degradation Process (LDDP) provides an explanation framework for sequential hard and soft failure modes. In this typical industrial product failure mode, the corresponding degradation phenomenon is presented as the product begins to degrade after a period of operation. For example, the process of crack propagation is a degradation process with a stochastic delay. Based on the LDDP method, we propose the Bayesian-LDDP model. Different from the LDDP method, which is based on the joint likelihood function for statistical inference, the Bayesian-LDDP method combines the prior distribution with the joint likelihood function to infer the posterior distribution of the parameters. Based on the posterior distribution, the Bayesian estimation and further reliability inferences can be derived. In this paper, the Bayesian-LDDP model is applied to the crack inspection data of a transport aircraft. Besides, inferences are provided under different combinations of the lifetime model and the degradation model. In terms of calculation, the Gibbs sampling algorithm is adopted for the Bayesian estimation of parameters. Furthermore, the best model that fits the set of data is chosen according to the DIC criterion. In addition, MCMC convergence diagnosis on the model is performed in this study, and further inference based on the posterior distribution is also implemented by using WINBUGS, including the confidence interval estimation of each parameter and the remaining useful life of the cracks.