Optimal maintenance time for repairable systems under two types of failures

A repairable system operates under a maintenance strategy that calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, failures are modeled according to a nonhomogeneous Poisson process. When the intensity function is assumed to grow proportional to a power of time, this process is called the Power Law Process. The motivation for this paper was a maintenance data set related to power switch disconnectors. Two different types of failures could be observed for these systems according to their causes. The major difference between these types of failures are their costs. Assuming that the system will be in operation for an infinite time, we find the expected cost per unit of time for each preventive maintenance policy and hence obtain the optimal strategy as a function of the intensity function of the process. Large sample procedures to estimate the optimal maintenance check points for the Power Law Process are also discussed. The results are applied in the power switch disconnector data set.