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This paper presents an extended EMQ model which determines an optimal production quantity for a single stage production system when defective items are stochastically produced in the production process and they are re-processed in the rework process to convert them into non-defectives. Through the mathematical modeling, an optimal solution minimizing the average cost per unit time and minimum average cost as well as some properties are derived. It can be shown that each of the existing models is a special case of the proposed model under some conditions. Numerical experiment is carried out to examine the behavior of the proposed model and support properties derived.