Analysis Of A Discrete Production Workstation

This paper introduces discrete production systems where units are produced one at a time. These systems exist in industry but to the best of our knowledge, they have not been addressed in the open literature. Manufacturing of large iron castings and special precast panels are examples of such production systems. We consider the case where the production process is imperfect resulting in non-conforming units that would be reworked. We assume that the rework process is imperfect and repeated as many times as needed until a conforming unit is produced or the production run ends. The outcomes of this process can be presented by a tree where each branch represents a sequence of production and rework attempts. We call each branch a scenario. The possible number of branches/ scenarios is enormously huge, even for reasonable production periods. We employ novel ideas to characterize all branches/scenarios in order to develop the probability mass function for the number of conforming units produced in a given length of the production period. We also, find the expected number of production attempts and rework attempts and the net cost of producing a conforming unit.