ON SOME MODELS OF GENERAL REPAIR

In this paper we continue to investigate the general repair models based on a virtual age concept. The studied model is constructed by the way that the repair affects the virtual age of a repairable system, Z(N) = A (Z(n-1) + X(Zn-1)), where A is a random variable, taking a value between 0 and 1, Z(n) is the virtual age after the nth repair, Xy is a random variable initiated by the distribution function (DF) of a failure time of a new system, F(x), with a DF of 1-(1 - F(x + y))/1 - F(y). It is shown that the corresponding renewal process converges in some sense to a renewal process with identically distributed cycles. When A = a is not random, some new monotonicity properties are proved.