Generalized geometric process and its application in maintenance problems

Since the repair effect may be varying with the number of repairs, we propose a generalized geometric process (GGP) to model the deteriorating process of repairable systems. For a GGP, the geometric ratio changes with the number of repairs rather than being a constant. Based on the GGP, two repair-replacement models are studied. Existing preventive maintenance (PM) models based on geometric process (GP) commonly assume that the PM is ‘as good as new’ in each working circle, which is not realistic in many situations. In this study, that the system is assumed to be geometrically deteriorating after PM or corrective maintenance (CM). Firstly, an age-dependent PM model is considered, in which the optimal policies N* and T* are obtained theoretically, and the optimal bivariate policy (N*, T*) which minimizes the average cost rate (ACR) can be determined by a searching algorithm. Next, because of the fact that the system deteriorates after maintenance, the schedule time to PM should decrease with the maintenance number increasing. Therefore, a sequential PM policy is investigated, and the optimal policy N* and the optimal schedule times T₁ ^*,T₂ ^*,…,T_N ^{* *} are computed. Finally, numerical examples are provided to illustrate the proposed models.