This paper develops an economic production quantity (EPQ) inventory model with rework process for a single stage production system with one machine. The existence of a unique machine results in limited production capacity. The aim of this research is to determine both the optimal cycle length and the optimal production quantity for each product to minimize the expected total cost (holding, production, setup, rework costs). The convexity of the inventory model is derived. Also the objective function is proved to be convex. The proposed inventory model is validated with illustrating numerical examples and the optimal period length and the total system cost are analyzed.