Approximate analysis of unreliable transfer lines with splits in the flow of material

This paper presents a Markov process model and an approximate decomposition technique for a discrete material transfer line with limited buffer capacity. A fraction of the parts processed at some stations in the line may be scrapped or reworked at dedicated machines to meet product quality requirements. Reworked parts are not sent back into the main line. This leads to splits in the flow of material. Processing times are deterministic and identical for all machines and are taken as the time unit. Machine specific times to failure and to repair are geometrically distributed. The model is analyzed through a decomposition into two-machine systems. We develop new decomposition equations for machines performing split operations. Production rates and inventory levels are computed and compared to simulation results. The results indicate that the method produces useful results for a variety of systems.