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Consider a system that should be continuously operating over an indefinitely long operation cycle n (…=,2,1n), where each operation causes a random amount of damage to the system, and these damages are accumulated with the current damage. The system fails when the total damage exceeds failure level ζ and a corrective maintenance (CM) is immediately conducted. To prevent such a failure, a preventive maintenance (PM) action should be performed. This paper considers a maintenance policy for such a system, in which the PM is carried out when the accumulated damage exceeds a pre-specified level δ (<ζ), or it is performed at the completion of Nth (…=,2,1N) operation, whichever comes first. Besides, a regular maintenance (RM) is also applied at every completion of operation in order to maintain the system for next use. The expected cost rate for an infinite time span is applied as a criterion for optimality. The optimal policies (i.e., *δ and *N) that minimize cost rates are derived analytically and computed numerically; useful properties and result discussions are presented, which indicate that the optimal maintenance policy is to perform PM only depend on the level of accumulated damage, it is unnecessary to depend on the number of operation (i.e., ∞→*N)

Optimal Maintenance Policy for a System Suffered Damage in Discrete Time Process