Residual-based inspection/replacement policy for a deteriorating system with Markovian covariates

This paper investigates a residual-based maintenance policy for a stochastic deteriorating system, which is influenced by a Markovian covariates process. The baseline stochastic deterioration is modeled by a Gamma process, and the covariates process is assumed to be a time-homogeneous finite-state Markov chain. A model similar to the proportional hazards model is used to represent the influence of the covariates. A residual-based inspection scheme, depending on the degradation level as well as the covariates state, is proposed. We derive the optimal maintenance threshold, optimal inspection scheme to minimize the expected average maintenance cost. By Monte Carlo simulations the efficiency of our method is studied.