The costs due to producing a product below the lower specification and above the upper specification limit are not equal in the production process. Due to these different costs, the total cost incurred will greatly depend on the process mean value. This study shows how the optimum value of production process mean can be obtained when the quality characteristic follows normal and non-normal distributions. In this study, optimization models for determining the optimum values of production process mean under different cost criteria are presented. A numerical example and sensitivity analysis are performed for each quality characteristic distribution.