Optimal maintenance policy for a Markovian system under periodic inspection

This study proposes a state-dependent maintenance policy R-ij(T, N, alpha) 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-ij(T, N, alpha), 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 less than or equal to a less than or equal to i - 1, i less than or equal to a less than or equal to j - 1 and j less than or equal to a less than or equal to 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. (C) 2001 Elsevier Science Ltd. All rights reserved.