Analytical properties of an imperfect repair model and application in preventive maintenance scheduling

The paper considers repairable systems under imperfect repair. The failure rate of a new system is assumed to follow a Weibull distribution and the repair efficiency is characterized by a Kijima type II virtual age model named Arithmetic Reduction of Age with infinite memory. An analytical approach to obtain the distribution of the inter-failure times is presented. The existence of a stationary regime is highlighted and the limiting distributions are explicitly derived. In this context, an optimal age-based preventive maintenance policy can be implemented. Three approaches are proposed, considering a static, a dynamic or a failure limit policy. Numerical simulations are presented to illustrate the policies.