Optimal Preventive Maintenance Policies for a System Suffered Damage in Discrete Time Process

Consider a system that should be operating at the time over an indefinitely long operation cycle. Each operation causes a random amount of damage to the system, and these damages are accumulated to the current damage to the system. A system fails when the total damage exceeds a failure level, and then a corrective maintenance (CM) should be made. To prevent such a failure, a preventive maintenance (PM) should be carried out. In addition, a regular maintenance (RM) action should be performed at every completion of operation cycle in order to maintain the system for the next operation. Two PM policies for such a system, one is operational number-dependent and the other is damage-dependent, are proposed and investigated as well as compared. The expected cost rate for an infinite time span is applied as a criterion of optimality. The optimal policies which minimize the cost rates are derived analytically and computed numerically, and useful properties and discussions for the results are presented.