Optimal maintenance time for imperfect maintenance actions on repairable product

This paper develops a maintenance strategy for repairable products that combines imperfect maintenance actions at pre-scheduled times and minimal repair actions for failures. Under a power law process of failures, an expected total cost is developed that involves the sum of the total cost of imperfect preventive maintenances and the expected total cost of minimal repairs. Moreover, a searching procedure is provided to determine the optimal maintenance schedule within a finite time span of warranty. When the parameters of the power law process are unknown, the accuracy of the estimated maintenance schedule is evaluated based on data through an asymptotic upper bound for the difference of the true expected total cost and its estimate. The proposed method is applied to an example regarding the maintenance of power transformers and the performance of the proposed method is investigated through a numerical study. Numerical results show that the proposed maintenance strategy could save cost whether an imperfect maintenance action or the perfect maintenance action is implemented.