A Bayesian estimation procedure for the non-homogeneous Gamma process

When the degradation growth of a unit depends only on its age, a widely accepted model to describe the degradation phenomenon is the non-homogeneous gamma process, which proved to be suitable to model such degradation phenomena as wear, fatigue, corrosion, crack growth, erosion, and consumption. In this paper, a Bayesian inferential procedure using the Markov Chain Monte Carlo technique is proposed for the non-homogeneous gamma process with power-law shape function. All the process parameters are left to be assessed, and prior information is formalized on some quantities having a "physical" meaning. Both vague and informative priors are provided. Point and interval estimation of the process parameters and of some functions thereof are developed, as well prediction on some observable quantities that are useful in defining the maintenance strategy is proposed. Finally, the proposed procedure is applied to a real dataset consisting of the sliding wear data of four metal alloy specimens.