Reliability-based maintenance optimization under imperfect predictive maintenance

The reliability-based maintenance optimization model has been focused by the engineers and scholars but it has never been solved effectively to formulate the effect of a maintenance action on the optimization model. In existing works, the system reliability was assumed to be increased to 1 after a predictive maintenance. However, it is very difficult in the most practical systems. Therefore, a new reliability-based maintenance optimization model under imperfect predictive maintenance (PM) is proposed in this paper. In the model, the system reliability is only restored to Ri (0<Ri <1, i∈N, N is natural number set) after the ith PM. The system uptimes and the corresponding probability in two cases whether there is an unexpected fault in one cycle are derived respectively and the system expected uptime model is given. To formulate the system expected downtime, the probability of each imperfect PM number in one cycle is calculated. Then, the system expected total time model is obtained. The total expected long-term operation cost is composed of the expected maintenance cost, the expected loss due to the downtime and the expected additional cost due to the occurrence of an unexpected failure. They are modeled respectively in this work. Jointing the system expected total time and long-term operation cost in one cycle, the expected long-term operation cost per time could be computed. Then, the proposed maintenance optimization model is formulated where the objective function is to minimize the expected long-term operation cost per time. The results of numerical example show that the proposed model could scheme the optimal maintenance actions for the considered system when the required parameters are given and the optimal solution of the proposed model is sensitive to the parameters of effective age model and insensitive to other parameters. The proposed model effectively solves the problem of evaluating the effect of an imperfect PM on the system reliability and presents a more practical optimization method for the reliability-based maintenance strategy than the existing works.