Renewal-geometric process is used to describe such a non-homogeneous deteriorating process that a system will deteriorate after several consecutive repairs, not after each repair described by the geometric process. In the maintenance domain, the effect of corrective maintenance after failure is generally not repairable as new (e.g. geometrically deteriorating). Preventive maintenance is critical before a system failure, due to economic losses and security threats caused by a sudden shutdown. Therefore, this article assumes that a system is geometrically deteriorating after corrective maintenance, wherein preventive maintenances sequence in the same repair period form a renewal process since it can restore the system to the initial state of the period. Furthermore, a binary policy [Formula: see text] is utilized to minimize the long-run average cost rate, where [Formula: see text] represents the number corrective maintenances and [Formula: see text] denotes the time interval between two consecutive preventive maintenances. In particular, pseudo-age replacement model represents a special case of [Formula: see text], which is considered as a generalization of the traditional age-based replacement model. Subsequently, the optimal policy [Formula: see text] can be verified in theory and an asymptotic optimal policy [Formula: see text] can be obtained based on a heuristic grid search. Finally, numerical examples verify the effectiveness of this proposed model and show that implementation of preventive maintenance for some repairable systems is superior to no preventive maintenance in both economic and reliability aspects.
A geometric-process maintenance model for a deteriorating system under a random environment