Analysis of a Discrete Material Unreliable Merge System with a Finite Intermediate Buffer and Three Stations with Operational -- Dependent and Idleness Failures

This paper examines a model of a flow line consisting of three unreliable machines and one buffer of limited capacity. The main assumptions of the model are the non linearity of the flow of material with the system performing merge operations and the new way of the machines reaching failure by allowing the machines to fail not only when they are operational but also when are either blocked or starved. The latter gives rise to the possibility of modeling the production of more than one part types by using this model as a decomposition block to solve large flow lines with merge operations and multiple part types. The model is solved analytically by developing a recursive algorithm that generates the transition matrix for any value C of the intermediate buffer capacity. Then various performance measures of the system (e.g., throughput) can be easily evaluated.