On the optimal degree of imperfect repair

A simple cost-wise comparison between the minimal and perfect repair of a system is discussed first using a relevant example. The main focus of this note, however, is on imperfect (general) repair. The best repair for our system in this case is defined as the one that corresponds to the optimal level (extent) of repair actions that minimize the long-run expected cost per unit of time. This complex optimization problem is considered for a specific imperfect repair model (Kijima II), using the developed earlier asymptotic approach to the corresponding virtual age modelling. It is shown that the optimal solution exists when the failure rate of a system tends to infinity as t tends to infinity and the corresponding cost function decreases sufficiently fast. An example illustrating the optimization procedure is considered.