Economic selection of mean value for a Multiple-Product-Manufacturing-Process with two-sided specification limits

We consider the problem of determining the optimum target value of the process mean for a manufacturing process where multiple products with two-sided specification limits are processed. Every item is inspected to determine whether the quality characteristic conforms to the lower and upper specification limits, and each nonconforming item is scrapped. Assuming that the quality characteristics of the products are normally distributed with a common process mean and known variances, an economic model is developed on the basis of the production, inspection, and scrap costs and the selling prices. The optimum value of the process mean is obtained by maximizing the expected profit. A method of obtaining the optimum solution is presented with an illustrative example of a metal plating process for three types of electronic devices Significance: The result of this study may be efficiently utilized for determining the common process mean for a manufacturing process where multiple products are processed.