Bayesian estimation and prediction for the transformed gamma degradation process

Very recently, a new degradation process model, named the transformed gamma process, has been proposed 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 introduces a Bayesian estimation approach for such a process, based on prior information on physical characteristics of the observed degradation process. Several different prior distributions are then proposed, reflecting different degrees of knowledge of the analyst on the observed phenomenon. A Monte Carlo Markov Chain technique is adopted to estimate the transformed gamma parameters and some functions thereof, such as the residual reliability of a unit, as well as to predict future degradation growth and residual lifetime. 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.