The optimum common process mean and screening limits for a production process with multiple products

In this research, we present a profit model for determining the most profitable common process mean and screening limits for a production process where multiple products are processed. Each outgoing item is inspected with a surrogate variable which is correlated with the quality characteristics of the products, and each item failing to meet the specification limits is scrapped. A profit model is constructed which involves selling prices, costs of production, inspection, and losses due to the penalty and scraps. The quality characteristics of the products are assumed to be normally distributed with known variances and an unknown common process mean to be determined. The optimum common process mean and screening limits are obtained by maximizing expected profit function using the Gauss-Seidel's iterative method. A numerical example is illustrated along with a sensitivity analysis of design parameters.