Optimum process mean setting based on variable sampling plan with producer’s and consumer’s risks

Abstract

In this paper, the author applies a variable sampling inspection plan with the producer’s and consumer’s risks on the operational characteristic curve for setting the optimum process mean. Assume that the quality characteristic of a one-sided lower specification limit product is normally distributed. The process standard deviation is known but the process mean is unknown. The rectifying inspection plan is adopted when the lot of product is rejected. The optimum process mean and the parameters of single variable sampling inspection plan are simultaneously determined by maximizing the expected total profit per unit under the specified producer’s and consumer’s risks. The numerical results show that (1) the unit price of product for the accepted lot, the production cost per unit, and the specification limit have a major effect on the expected total profit per unit; (2) the process standard deviation and the lot tolerance percent defective have a moderate effect on the expected total profit per unit

Keywords:

• Variable sampling inspection plan
• Producer’s risk
• Consumer’s risk
• Process mean