absorbing markov chain models to determine optimum process target levels in production systems with rework and scrapping

in this paper, absorbing markov chain models are developed to determine the optimum process mean levels for both a single-stage and a serial two-stage production system in which items are inspected for conformity with their specification limits. when the value of the quality characteristic of an item falls below a lower limit, the item is scrapped. if it falls above an upper limit, the item is reworked. otherwise, the item passes the inspection. this flow of material through the production system can be modeled in an absorbing markov chain characterizing the uncertainty due to scrapping and reworking. numerical examples are provided to demonstrate the application of the proposed model.