Hybrid hazard rate model for imperfect preventive maintenance of systems subject to random deterioration

This paper deals with imperfect preventive maintenance optimization problem. The system to be maintained is assumed to be subject to random deterioration. To reduce the risk of failures, the proposed maintenance model takes into account two type of maintenance actions, namely corrective maintenance (CM) and preventive maintenance (PM). The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modeled on the basis of the hybrid hazard rate model. The objective of the proposed imperfect PM optimization model consists on finding the optimal reliability threshold together with the optimal number of PM actions to minimize the expected total maintenance and replacement cost per unit of time. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is also given to illustrate the proposed maintenance model.