Imperfect repair models with preventive maintenance

Brown and Proschan (1983) introduced the imperfect repair model, in which an item, upon failure, is replaced with a new one with probability (alpha), and is minimally repaired with probability 1-(alpha). In this paper we equip the imperfect repair model with preventive maintenance, and we obtain stochastic maintenance comparisons for the numbers of failures under different policies via a point-process approach. We also obtain some results involving stochastic monotonicity properties of these models with respect to the unplanned complete repair probability (alpha).