Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers

This paper models and analyzes multi-stage transfer lines with unreliable machines and finite buffers. The machines have exponential operation, failure, and repair processes. First, a mixed vector–scalar Markov process model is presented based on some notations of mixed vector–scalar operations. Then, several steady-state system properties are deduced from this model. These include the reversibility and duality of transfer lines, conservation of flow, and the flow rate–idle time relationship. Finally, a four-stage transfer line case is used to compare and evaluate the accuracy of some approximation methods presented in the literature with the exact numerical solutions this model can provide. The properties and their proofs in this paper lay the theoretic foundation for some widely held assumptions in decomposition techniques of long transfer lines in the area of manufacturing systems engineering.