Optimum tolerance design using component-amount and mixture-amount experiments

The tolerance design problem involves optimizing component and assembly tolerances to minimize the total cost (sum of manufacturing cost and quality loss). Previous literature recommended using traditional response surface methodology (RSM) designs, models, and optimization techniques to solve the tolerance design problem for the worst-case scenario in which the assembly characteristic is the sum of the component characteristics. In this article, component-amount (CA) and mixture-amount (MA) experiment approaches are proposed as more appropriate for solving this class of tolerance design problems. The CA and MA approaches are typically used for product formulation problems, but can also be applied to this type of tolerance design problem. The advantages of the CA and MA approaches over the RSM approach and over the standard, worst-case tolerance-design method are explained. Reasons for choosing between the CA and MA approaches are also discussed. The CA and MA approaches (experimental design, response modeling, and optimization) are illustrated using real examples.