In this paper we consider closed flow line systems with samploing inspections. The total number of parts in the system is assumed to be N. The processings carried out of each station do not always meet the requirement of quality. Therefore, upon completion of its processing at each station, a part is inspected to determine whether the processings meet the requirement of quality or not. We assume that inspection are done on a random basis. If a part is found to be defective by an inspection, it is fed back to the apropriate station. Two different cases will be considered in this study : a three-station flow line system with infinite buffers and a two-station flow line system with finite buffers. For each case, we will develop an exact method to obtain the performance measures such as throughput, machinen utilization, average outgoing quality and manufacturing lead time. For the case of the two-station flow line system ith finite buffers, we will also develop an approximation method using a stage-aggregation technique. Then using buffers, we will also develop an approximation method using a stage-aggregation technique. Then using these results, we will try to find an optimal inspection policy which maximizes the expected net profit under a certain cost structure. Although we present the results only for the two or three station flow line system in this paper, the results obtained in this paper can be extended easily to the system which consists of more than two or three stations.