Preventive Maintenance Models Based on the Generalized Geometric Process

For a generalized geometric process (GGP), the geometric ratio changes with the number of repairs rather than a constant. The GGP is a more flexible maintenance model that can reflect the varying of the repair effect to the system. On the basis of the GGP, two imperfect preventive maintenance (PM) models are studied. First, we assume that the system is preventively maintained periodically after every $T$ time unit, and is correctively repaired at failure. The corrective repair is a minimal repair that just restores the system to work, while the PM results in a GGP, i.e., the lifetime sequence of a system after PM constitute a decreasing GGP. The long-run average cost rate $C(N,T)$ of the system is derived, and the optimal bivariate policy $(N^*,T^*)$ is determined by minimizing $C(N,T)$ , where $N$ is the number of PMs before replacement. Next, a sequential PM model is investigated for a system in which a sequential time interval to be determined for PM. An algorithm is given to seek the optimal replacement policy $N^*$ and the optimal time intervals $T_1^*,T_2^*,\ldots, T_N^*$ between PMs. By assuming that the lifetime of the system is Weibull distributed, the optimal policy is obtained explicitly. In both models, numerical examples are provided to verify the effectiveness of the approaches developed.