A Markovian approach to determining optimum process target levels for a multi-stage serial production system

Consider a production system where products are produced continuously and screened for conformance with their specification limits. When product performance falls below a lower specification limit or above an upper limit, a decision is made to rework or scrap the product. The majority of the process target models in the literature deal with a single-stage production system. In the real-world industrial settings, however, products are often processed through multi-stage production systems. If the probabilities associated with its recurrent, transient and absorbing states are known, we can better understand the nature of a production system and thus better capture the optimum target for a process. This paper first discusses the roles of a Markovian approach and then develops the general form of a Markovian model for optimum process target levels within the framework of a multi-stage serial production system. Numerical examples and sensitivity analysis are performed.