A production line with a limited number of carts or pallets is regarded as a closed loop manufacturing system. Such production lines are very useful in various manufacturing systems, such as semiconductor production systems. In this paper, we study a two-loop closed production system by means of block-structured Markov chains, and propose an effective RG-factorization solution to evaluate performance measures of the system, including throughput and WIP level. Based on this, the system can be numerically analyzed with respect to several crucial parameters. This leads to improvement on the design of the carts quantities, which are always crucial factors in closed-loop production lines.