Optimal process mean and standard deviation settings for rectifying sampling inspection plan with quality investment

In this paper, the rectifying sampling inspection plan with quality investment for the product lot is used in the determination of optimal process mean and standard deviation. Consider the quality characteristic of product is normally distributed with both unknown process mean and unknown standard deviation. The product lot is sold to the different markets according to the defective numbers of sample. Assume that the declining exponential reduction of process mean and standard deviation is the function of quality investment. For a given rectifying inspection plan, one can obtain the optimal quality investment and corresponding improved process mean and standard deviation based on the maximum expected total profit of product lot per unit.