Bayesian Inference for the Bounded Transformed Gamma Process

Very recently, a novel stochastic process model, called the bounded transformed gamma process, has been proposed to describe bounded degradation phenomena, where the degradation level can not exceed a given upper bound, due to inherent features of the degradation causing mechanism. In this paper, a Bayesian estimation procedure is developed and illustrated for such a stochastic process, which uses prior information on the upper bound and on other physical characteristics of the degradation phenomenon under observation. Several experimental scenarios are considered and, for each of them, specific prior distributions are suggested which allow to convey into the inferential procedure the different information the analyst is assumed to possess. A Monte Carlo Markov Chain method is developed to estimate the process parameters and some functions thereof, such as the mean degradation level, the residual reliability of a unit, and to predict the future degradation growth. Finally, the proposed procedure is validated on a set of real data containing wear measurements in different time instants of the liners of an 8-cylinder Diesel engine for marine propulsion.

Keywords: Transformed gamma process, Bounded degradation phenomena, Bayesian estimation, Monte Carlo Markov chain method, Remaining useful life, Residual reliability.

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