A time-discrete extended Gamma process for deterioration processes

A widely used model to describe deterioration processes, whose growth rate depends only on the age of the item and not on the accumulated damage, is the non-stationary Gamma process. This process, however, is not a proper choice when there is an empirical evidence that the variance-to-mean ratio of the process varies with time. In this paper, we propose a generalization of the non-stationary Gamma process which can be viewed as a time discretization of the extended Gamma process. The proposed model allows one to describe time-dependent deterioration processes whose variance varies with time, not necessarily in proportion to the mean. Both an estimation procedure of the model parameters and a test for assessing whether the assumption of the Gamma process can be rejected or not are discussed. The proposed model has been applied to a real dataset consisting of the sliding wear data of four metal alloy specimens.