The Near-Optimal Preventive Maintenance Policies for a Repairable System with a Finite Life Time by Using Simulation Methods

For a repairable and deteriorating system, the theoretical preventive maintenance (PM) models are usually complicated and need numerical methods to obtain the optimal PM policies since the system’s failure rate function is changed after each PM. It makes the application of the theoretical model not quite suitable for real cases. Moreover, the theoretical optimal PM solution is obtained by evaluating the expected cost rate of the system over an infinite time span. Yet, in reality, a deteriorating system always has a finite life time. Hence, searching for an optimal PM solution for a deteriorating system over an infinite time span might not be rational. Therefore, we consider using Monte Carlo simulation method to mimic the complicated failure process of a system with PM activity and then to obtain a range of the near-optimal PM policies. In this paper, the inverse transformation method and the rejection method are applied to generate the time-between-failures (TBF) random variates. The algorithms for generating the RVs are developed. The procedure of finding the nearoptimal PM policies are also provided. Then, examples of using the proposed simulation method to obtain the nearoptimal policies for the age-reduction PM model in a finite time span are presented and discussed.