The Inverse Gamma process for modeling state-dependent deterioration processes

This paper proposes a non-stationary Inverse Gamma process for modeling state- dependent deterioration processes with non linear trend. The proposed processes are mathematically more tractable than previously proposed state-dependent processes because, unlike the previous models, the Inverse Gamma process is a time-continuous and state-continuous model and does not require discretization of time and state. The conditional distribution of the deterioration growth over a generic time interval, the conditional distribution of the residual life and the residual reliability of the unit, given the current state, are provided. Maximum likelihood estimates of the parameters which index the proposed process are also discussed. Finally, the proposed model is applied to the wear process of the liners of some Diesel engines which was previously analyzed and proved to be a purely state-dependent process. The comparison of the inferential results obtained under the competing models shows the ability of the Inverse Gamma process to adequately model the observed state-dependent wear process.