An unreliable single part type transfer line with fixed inter machine buffer sizes is considered. In general, imperfect machines operating with imperfect raw material, or partially processed raw material, will result in the production of a mix of conforming and non conforming parts. The problem of optimal joint assignment of buffer sizes and inspection station positions is here considered where we assume that defective parts are scrapped upon detection. The performance measure to be optimized is a combination of work in process storage and parts inspection costs, with an eye to determining the adequate number of inspection stations. We propose an exact method for solving this problem and large-scale numerical experiments are provided to demonstrate the efficiency of the proposed algorithm. Interesting properties of the problem are also denoted based on our empirical results.