The optimal limit of the number of consecutive minimal repairs

Abstract

Brown and Proschan(1983) introduced a model for imperfect repair. At each failure of a device, with probability p, it is repaired completely or replaced with a new device(perfect repair), and with probability 1-p, it is returned to the functioning state, but it is only recovered to its condition just prior to failure(imperfect repair or minimal repair). In this paper, we limit the number of consecutive minimal repairs by n. We find some useful properties about $\mu$ 수식 이미지$_{k}$ 수식 이미지, the expected time between the k-th and the (k+1)-st repair under he assumption that only minimal repairs are performed. Then, we assign cost to each repair and find the value of n which minimized the long-run average cost for a fixed p under the condition that the life distribution F os the device is DMRL.L.