Base Stock system for patient customers in inventory control is a special type of problem which introduces the fact that the shortages do not result in the loss of profit due to the fact that immediately a demand for the product is reported; an order is placed for supply. This is in addition to the inventory on hand called the ground level inventory. Hence the socalled base stock denoted as B is equal to the total of the inventory on ground and the inventory on orders placed. In this paper the optimal value of B is obtained using the fact that the lead time is a random variable and it satisfies the so called Setting the Clock Back to Zero (SCBZ) property which amounts to the change in the parameter of the lead time distribution after a change point.