Optimum target values for two machines in series with 100% inspection

In this paper, we consider a manufacturing system with two machines in series. The manufactured product is assumed to have two attributes which are related to the processing of the product, by machine 1 and machine 2 respectively (a product attribute could be weight, diameter, width, length, thickness, tensile strength, electrical resistance, etc.). Each attribute has a lower specification limit (LSL) set for it, and if the measured attribute for a certain product is less than its LSL, the product is recycled at a certain cost. A mathematical model is developed for finding the optimum setting point for each machine. A numerical approach is suggested for solving the model, and a numerical example is provided.