Age-reduction models for imperfect maintenance

Maintenance of a deteriorating system is often imperfect, with the state of the system after maintenance being at a level somewhere between new and its prior condition. In this paper, the concept of reduction in virtual or effective age is used to model the effect of both imperfect corrective maintenance (CM) and imperfect preventive maintenance (PM). Results from counting-process theory then produce a likelihood function necessary for parameter estimation, and the method is tested on known maintenance data. Finally, it is shown how to evaluate, by simulation, the expected number of system failures up to time t under a given periodic PM strategy. This measure is incorporated into a cost rate function which is then minimized to find the optimal length of a PM interval and the optimal number of PMs to carry out before system replacement.