In this paper we analyze a two-stage inspection system. There are two stations numbered 1 and 2, in tandem. An infinite number of jobs always waits in front of station 1 and there is a finite buffer space between stations 1 and 2. If a processed (inspected) job at station 1 is defective, it is rejected ; otherwise it proceeds to station 2. Station 2 in operates the same manner. Both stations process m jobs at a time and there may be failures during each processing time. In this mode of operation station 1 will at any time be busy or blocked and station 2 will be busy or idle. An important problem for such a system is how to improve the production rate by increasing the buffer space. We attempt to formulate this problem as a Markov chain. It is shown that the buffer size should be larger than the batch service size, m. Futhermore, we propose an approximation formula for the production rate. Numerical examples are presented which support the usefulness of the approximation.