Cost evaluation for an imperfect-repair model with random repair time

A repair can bring the state of a failed system to a level which is somewhere between new and prior to repair. In most repair models proposed in the literature so far, the repair time is assumed to be negligible, and so the length of repair time has not been a factor in developing the maintenance models. However, it is more realistic to assume that it takes a certain amount of repair time. In this paper, we discuss an imperfect repair model with random repair times. We first derive a formula that can be used to evaluate the expected numbers of perfect and minimal repairs. The expected costs during (0, t ], t >0 fixed, are also evaluated based on the convolution of the failure and repair distributions of the system.