Optimum process mean setting based on variable sampling plans with specified consumer's risk

In the present paper, a new economic design with variable single sampling inspection plan for determining the optimal process mean is presented. The quality characteristic with the one-sided lower specification limit is assumed to be normally distributed with unknown mean and known standard deviation. The 100% rectifying inspection plan is adopted when the product lot is rejected. The optimum process mean and the parameters of sampling inspection plan are simultaneously determined by maximizing the expected total profit per unit and meeting the requirement of the specified consumer's risk. Two numerical examples and sensitivity analyzes of parameters are provided for illustration. The numerical results show that, among the model parameters, the price of product for accepted lot, the processing cost per unit, and the lower specification limit significantly affect the expected total profit per unit.