In this paper we consider a general type of repair model which weakens the influence of all previous failure history of the system Let T, denote the time interval between the (n - 1)-st failure and n-th one and X , denote the age of the system after performing the n-th repair. We propose the following two assumptions that T , is statistically dependent on X n- and X, is dependent on X n- and T,. This is general repair model includes minimal repair, perfect repair and other special cases. It is well-known that the distribution and expectation of interval time T, in minimal repair model is monotonically decreasing in n if F(t) = p[T₁≤t] belongs to either group of distribution among IFR, DMRL, etc.. As an alternative for these groups, we here present new groups of distribution which decrease the distribution and expectation of T , in our general repair model. Further, according to the period of replacement determined by the age of the system, a replacement d e l with general repair is considered In this model, we discuss the condition of the marginal distribution under which an optimum replacement period exists for minimizing the total long-run average cost per unit time.