Modeling of Bernoulli production line with the rework loop for transient and steady-state analysis

Production system modeling (PSM) aims to reveal the fundamental principles of production procedures. Most of the research efforts for PSM focus on serial production lines, which is the most fundamental structure in a production system. However, modeling regarding more complex production systems is less developed. Decomposition methods are commonly used to study complex production lines; however, these approaches are only capable of handling steady-state situations. Current closed-form transient modeling cannot be directly applied to production systems with rework loops. In this paper, an analytical method for modeling a production system with a rework loop is presented. Furthermore, a novel 'Self-View' method is proposed for obtaining both transient and steady-state results. This research extends the PSM transient analysis to more complex production lines and overcomes restrictions of machine reliability and buffer capacity in the rework loop. The transient performance measures, i.e., the number of iterations and the settling time, are investigated. Moreover, sensitivity studies of starvation, blockage, production rate, and work-in-process on rework rate are conducted. As a result, the proposed 'Self-View' method in this research shows promising potential for modeling other complex production systems.