This papaer analyzes a system with consists of two workstations that are separated by finite buffer storage. In this system, we assume that the processing time in each station in a random variable and each station is not vulnerable to failure. To control the in-process inventory in the serial production system we use the (R, r) policy which is similar to the (s, S) policy in the inventory theory. Under the (R, r) policy the preceding station is forced down when the inventory level in the buffer reaches R and starts operation again when the inventory level falls to r. For the model developed, we analyze the system characteristics and the system performances.