Optimal maintenance policy for a system subject to damage in a discrete time process

Consider a system operating over n discrete time periods (n=1, 2, …). Each operation period causes a random amount of damage to the system which accumulates over time periods. The system fails when the cumulative damage exceeds a failure level ζ and a corrective maintenance (CM) action is immediately taken. To prevent such a failure, a preventive maintenance (PM) may be performed. In an operation period without a CM or PM, a regular maintenance (RM) is conducted at the end of that period to maintain the operation of the system. We propose a maintenance policy which prescribes a PM when the accumulated damage exceeds a pre-specified level δ (<ζ), or when the number of operation periods reaches N, whichever comes first. With the long-term average cost rate as an optimality criterion, we optimize the maintenance policy parameters δ⁎ and N⁎ and discuss some useful properties about them. It has been shown that a δ-based PM outperforms a N-based PM in terms of cost minimization. Numerical examples are presented to demonstrate the optimization of this class of maintenance policies.