An approximate analytical method for evaluating the performance of closed-loop flow systems with unreliable machines and finite buffers

We present an efficient and accurate approximate analytical decomposition method for evaluating the production rate and distribution of inventory of a closed-loop manufacturing system with unreliable machines and finite buffers. It is based on an earlier decomposition for a tandem line; it differs only in accounting for the different sets of machines that could cause blockage or starvation to other machines. The method can be applied to tandem production lines with a limited number of pallets or fixtures; the pallets travel in a closed loop even though the parts do not. It can also be applied to systems controlled by a CONWIP policy with infinite or finite buffers since such a policy can be implemented with a limited number of tokens that behave in the same way as pallets.