Closed-Loop Production Lines With Geometric Reliability Machines: Modeling, Analysis, and Application

Closed-loop production lines with constant number of carriers are widely encountered in manufacturing systems. In this letter, we introduce an iteration method to study the key performance indicator (KPI) of closed-loop production lines with geometric reliability machines. First, analysis of two-machine loops is carried out to derive the distribution of carriers in the system. Then the larger loop systems are decomposed into multiple smaller loop lines hierarchically until two-machine loops are obtained. Through an iteration procedure, the interactions between the small loops are estimated to adjust the carrier distributions using the two-machine formula. When the procedure converges, the system KPI, i.e., line production rate, can be estimated. It is shown that the procedure is convergent and results in high accuracy of estimation. Finally, an application study at an automotive body shop is presented.