Determination of the economical target value through sampling inspection

We consider the determinant of the most economical target value through the sampling inspection by two consecutive machines. The machine sequence is fixed as products have to be processed by machine 1 first and then by machine 2 next. In this paper, we assume that if quality of a unit is lower than inspection lower specification limited, then the product is not accepted. Otherwise, it is accepted. And we assume that the quality characteristic is larger-the-better characteristic and its distribution is the normal distribution whose standard deviation is known. This paper ends up with a numerical example by using the total expected profit function model that considers the scales profits, inspection costs and material costs. And we analyze the variation of the total expected profit by changing coefficients of the functions.