Optimal Weighted Approach in Dual-Response Surface Optimization

Dual-response surface method is a powerful method for simultaneously optimizing the mean and the variance of responses in quality engineering, in which the minimization of the mean squared error (MSE) is an effective approach. To date, the relative weights of bias and variance have been equally set or determined only by the data. However, the weights should be determined according to the tradeoffs on decision maker´s preference. In this paper, we proposed an optimal weighted mean squared error (MSE) approach to determine the weights of bias and variance based on both a decision maker´s preference structure and the data. In addition, examples are given to illustrate the proposed approach and compared with other existing procedures.