Bayesian estimation and prediction for the transformed Wiener degradation process

This paper proposes some Bayesian inferential procedures for the transformed Wiener (TW) process, a new degradation process that has been recently suggested in the literature to describe degradation phenomena where degradation increments are not necessarily positive and depend stochastically on the current degradation level. These procedures have been expressly conceived to allow one incorporating into the inferential process the type of prior information, on meaningful physical characteristics of the observed degradation process, that is generally available in practical settings. Several different prior distributions are proposed, each of them reflecting a specific degree of knowledge on the observed phenomenon. Simple strategies for eliciting the prior hyper-parameters from the available prior information are provided. Estimates of the TW process parameters and some functions thereof are retrieved by adopting a Monte Carlo Markov Chain technique. Procedures that allow predicting the degradation increment, the useful life of a new unit, and the remaining useful life of a used unit are also provided. Finally, an application is developed on the basis of a set of real degradation measurements of some infrared light-emitting diodes, widely used in communication systems. The obtained results demonstrate the feasibility of the proposed Bayesian approach and the flexibility of the TW process.