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