Computing trade-offs in robust design: Perspectives of the mean squared error

Researchers often identify robust design as one of the most effective engineering design methods for continuous quality improvement. When more than one quality characteristic is considered, an important question is how to trade off robust design solutions. In this paper, we consider a bi-objective robust design problem for which Pareto solutions of two quality characteristics need to be obtained. In practical robust design applications, a second-order polynomial model is adequate to accommodate the curvature of process mean and variance functions, thus mean-squared robust design models, frequently used by many researchers, would contain fourth-order terms. Consequently, the associated Pareto frontier might be non-convex and supported and non-supported efficient solutions needs to be generated. So, the objective of this paper is to develop a lexicographic weighted-Tchebycheff based bi-objective robust design model to generate the associated Pareto frontier. Our numerical example clearly shows the advantages of this model over frequently used weighted-sums model.