Under the imperfect repair model of Brown and Proschan (1983), a failed item is replaced by a new item (perfect repair) with probability p, and with probability 1 $-$ p, a minimal repair is performed; that is, the failed item is replaced by a working item of the same age. This procedure is repeated at each subsequent failure. Block, Borges, and Savits (1985) extend this model by allowing p to be a function of the age of the item. In both of these models, imperfect repairs are thus assumed to be minimal. Whitaker and Samaniego (1989) propose an estimator for the life distribution, F, of a new item, when either of these processes is observed until the time of the $m sp{ rm th}$ perfect repair.
