Mean Square Error Criteria to Multiple Quality Characteristics Robust Design by the Weighted Tchebycheff Method
Robust design has been widely applied in quality improvement. For most products, quality is multidimensional. Little attention has been paid to multiple quality characteristics robust design (MQCRD). MQCRD mainly faces two problems: measurement model and multiple objectives optimization. In order to give an appropriate measurement criterion and generate better Pareto solutions, a MQCRD model by the Weighted Tchebycheff method based on the mean square error (MSE) criterion is proposed. Firstly the MSE estimations for each quality characteristic are obtained by response surface method (RSM) and a MQCRD model based on the MSE criteria is given. Then a MQCRD model by the Weighted Tchebycheff method is present, which minimizes the distance between objective functions and the idea point based on the weighted infinite norm. The proposed approach could find very efficient Pareto solutions. Illustrative example shows the model can generate more efficient and robust solutions than the weighted-sum approach. Furthermore it has better results than the generalized reduced gradient (GRG) and quadratic loss function approach.
L.Y. Xie, M.N. James, Y.X. Zhao and W.X. Qian
L. J. Shen et al., "Mean Square Error Criteria to Multiple Quality Characteristics Robust Design by the Weighted Tchebycheff Method", Advanced Materials Research, Vols. 118-120, pp. 881-885, 2010