We consider an optimal ordering policy of a system subject to shocks w
ith number-dependent minimal repair and random lean time. By introduci
ng costs due to ordering, repairs and shortage, we derive the expected
cost per unit rime in the long I un as a criterion of optimality and
seek the optimum ordering policy by minimizing that cost. We show that
, under certain conditions, there exists a finite and unique optimum p
olicy. Various special cases are discussed. A numerical example is giv
en to illustrate the method.