A Bayesian approach for the transformed gamma degradation process

Very recently, a new degradation process, namely the transformed gamma (TG) process, has been proposed in the literature to describe Markovian degradation processes whose increments over disjoint intervals are not independent, so that the degradation growth over a future time interval can depend both on the current age and the current state (degradation level) of the unit. This paper proposes a Bayesian estimation approach for such a process, that is based on prior information relative to the sign (positive or negative) of the correlation between the degradation increment and the current state or age of the unit. Several dierent prior distributions are then proposed, re ecting the knowledge of the analyst. A Markov Chain Monte Carlo technique, based on the adaptive Metropolis algorithm, is used for estimating the TG parameters and some functions thereof, such as the residual reliability of a unit, as well as for predicting future degradation growth. Finally, the proposed approach is applied to a real dataset consisting of wear measures of the liners of the 8-cylinder engine which equips a cargo ship.