Bayesian methods for bounded transformed gamma degradation processes with different age and state functions

To better describe stochastic degradation processes of real technological units, which are typically bounded for physical reasons, a particular version of the transformed gamma process (TGP), the so called bounded transformed gamma process (BTGP), has been recently proposed. Like the TGP, the BTGP is obtained, from the gamma process, by transforming the scales of time and the state via two functions, named the age and the bounded state functions. Different functional forms of those functions are available in literature, and the most suitable ones are to be selected to fit the available wear data with the aim of predicting the remaining useful life and estimating the residual reliability of the technological units under study. In this work, we apply a Bayesian method, namely the Bayes factor, to select the functional form of the bounded state function that provides the best fit of the degradation data under study, and that can be indexed up to three parameters. The proposed model selection procedure is able to exploit prior information held by the experts from previous experience. More specifically, we use some knowledge on the upper bound of the degradation phenomenon and on the shape of the mean degradation function. Some Markov chain Monte Carlo techniques are adopted for the analysis, and then validated on a real data set consisting of some wear measurements of the liners of an engine of a cargo ship.