Integrating a bi-objective paradigm to tolerance optimization

The primary goal of tolerance design is to determine the optimal tolerance by minimizing quality loss and process costs (i.e. manufacturing and rejection costs). Most tolerance design models find the optimal tolerance by considering a sum of process quality and costs. In real-world industrial settings, however, quality practitioners often need a balance associated with the quality and costs. For this reason, a bi-objective tolerance optimization problem for obtaining the Pareto solutions of the quality and costs need to be considered. In practical situations, objective functions in many tolerance optimization models reported in the research community often become a high-order, and the associated Pareto frontiers can be non-convex. Thus, it is known that obtaining efficient solutions using the conventional weighted-sum method widely used in tolerance optimization is unlikely. To address this concern, we develop a weighted-Tchebycheff based bi-objective tolerance design model to obtain all efficient solutions and a non-convex Pareto frontier. The weighted-Tchebycheff method is far more effective than any other when a function has higher-order terms or is neither convex nor concave. A numerical example is provided, and a comparison between the two methods is made.