High quality assembly products are produced by a matching method in machining-assembly production systems. If we use an accuracy policy in the part selection policy which is applied to a ball-bearing manufacture, the part flow stagnates and buffer storage is necessary to increase the production rate. Furthermore, in some combinations of part machining error distributions buffer storage is not useful, and the production rate drops. In this paper, we study the optimum part selection policy which yields the maximum production rate using a Markov decision process. Next, we study the characteristics of the optimum policy, and show the effectiveness of the policy by comparing the production rates yielded in the systems by the policy and the accuracy policy. Finally, we discuss the flexibility of the optimum policy. From the analysis, it is presented that the optimum part selection policy is very effective to increase the production rate, and in every combination of part machining error distributions the policy yields the ideal maximum production rate.