Optimal replacement policy for a repairable system with deterioration based on a renewal-geometric process

The optimal replacement policy is proposed for a new maintenance model of a repairable deteriorating system to minimize the average cost rate throughout the system life cycle. It is assumed that the system undergoes deterioration with an increasing trend of deterioration probability after each repair. More specifically, a novel maintenance model is first presented based on a new defined renewal-geometric process, which splits the operation process into an early renewal process and a late geometric process to characterize such a special deterioration delay. Then, the average cost rate for the new model is formulated according to the renewal-reward theorem. Next, a theorem is presented to derive the theoretical relationships of optimal replacement policies for the geometric-process maintenance model and the new proposed model, respectively. Finally, numerical examples suggest that the optimum values can be determined to minimize the average cost rates.