Threshold Type Maintenance Policies for Systems under Cumulative Damage from Random Shocks

Abstract

An optimal maintenance policy was investigated for deteriorating systems subjected to shocks caused by a non-homogeneous Poisson process. The systems become damaged to an extent if the magnitude of the shocks exceeds a deterioration state-dependent limitation. The extent of the damage caused by the shocks was assumed to be identically distributed, and independent of the counting process for shocks. System deterioration was modeled as a discrete-time Markov chain, with the state transition probabilities depending on cumulative damage. The system was treated as a failure if the cumulative damage reached a critical level. At the beginning of each time period, the decision maker selected one action from three possible actions: operate, repair, or replace. The optimal decision-making was formulated as a Markov decision process. An optimal maintenance policy that minimizes the total discounted expected cost over an infinite horizon was determined on the basis of information related to system deterioration and the cumulative damage. The optimal maintenance policy was shown to have a threshold-type structure under certain conditions for deterioration and cost. This structural property is helpful for determining an optimal maintenance policy.