In this article, we deal with an economic production quantity (EPQ) problem for an unreliable production facility where the production rate is more than the demand rate. The machine is subject to stochastic break down. In this paper, the basic EPQ model is formulated under general failure and general repair time distributions and the optimal production-purchase policy is derived for exponential failure and exponential repair time distributions. Considering randomness of the time to machine failure and corrective repair time, the model is extended to the case where purchasing inventory may be useful to satisfy customer demands. That is, at each cycle, we may be required to purchase and produce items. Therefore, decision variables are amount of purchase and production. Optimal production-purchase policy of the proposed model is derived numerically by using MATLAB and the sensitivity of the optimal results with respect to those parameters which directly influence the machine failure and repair rates is also examined. Finally, to illustrate the efficiency of new approach, the results obtained from new approach are compared to Giri model.