Optimal maintenance policy for a Markovian system under periodic inspection

This study proposes a state-dependent maintenance policy R_i,j(T,N,α) for a multi-state continuous-time Markovian deteriorating system subject to aging and fatal shocks and with states 0 (new state) <1<2<…<L (failed-state). Under R_i,j(T,N,α), the system is inspected at each kT for k=1,2,3… to identify the current state as, say a, and then do-nothing, repair and replacement are taken immediately according to 0≤a≤i−1, i≤a≤j−1 and j≤a≤L−1, respectively in case i<j. Additionally, the replacement is carried out whenever L occurs due to fatal shocks. This policy includes numerous maintenance policies in the literature as special cases and can be applied quite generally. We then try to determine the optimal i^*, j^* and T^* such that the expected long-run cost rate is minimized. A numerical example is given to evaluate the performance of the policy.