Some results for repairable systems with general repair

In this paper, we develop general repair models for a repairable system by using the idea of the virtual age process of the system. If the system has the virtual age V n – 1 = y immediately after the ( n – l)th repair, the n th failure-time X n is assumed to have the survival function where is the survival function of the failure-time of a new system. A general repair is represented as a sequence of random variables A n taking a value between 0 and 1, where A n denotes the degree of the n th repair. For the extremal values 0 and 1, A n = 1 means a minimal repair and A n = 0 a perfect repair. Two models are constructed depending on how the repair affects the virtual age process: V n = V n – 1 + A n X n as Model 1 and V n = A n ( V n – 1 + X n ) as Model II. Various monotonicity properties of the process with respect to stochastic orderings of general repairs are obtained. Using a result, an upper bound for E S n when a general repair is used is derived.