Analysis of a three machine-one buffer merge system with quality and operational failures

Abstract

This paper examines a three machine- one buffer merge system with quality and operational failures. It is assumed that the buffer has two immediate preceding machines, performing the same operations and one immediate succeeding machine that receive material from the buffer. For the case where the buffer reaches its own capacity, one of the two preceding machines has priority over the other to dispose its processed part into the buffer. Processing times are assumed to be deterministic and identical for all machines and are taken as the time unit. Operational, quality failures and repair probabilities are geometrically distributed. All possible transition equations for the examined model are derived and a recursive algorithm that generates the transition matrix for any value N of the storage level is developed. Such a model can be used as a building block in a decomposition method for the performance evaluation of large production systems with split/merge operations (for example, flow lines with rework loops).