In this paper, we consider that the working environment has certain states, and in every state, the parameters of quality characteristics are different. Thus, if we set the characteristics parameters in a specified state, these parameters will change to another state. To describe this situation, we use a mixture of normal distributions, which comprise a flexible and powerful statistical-based modeling tool in practice. Under the step loss function and the piecewise linear loss function, we select the optimal means for the proposed manufacturing process