An I-optimal experimental design-embedded nonlinear lexicographic goal programming model for optimization of controllable design factors

Optimal experimental designs are effective offline quality improvement techniques used to enhance existing products and develop new products for a constrained design region. For some practical situations, I-optimal experimental designs may be the most suitable way to construct optimal experimental design points, by addressing prediction variance to generate a measure of prediction performance over the non-standard experimental design region. The purpose of this article is three-fold: (1) the I-optimality criterion is selected for minimizing the average prediction variance; (2) fitted mean and variance response models are found; and (3) a nonlinear lexicographic goal programming model incorporating an I-optimal experimental design is proposed to find the optimum settings of controllable design factors. Comparison studies and a numerical example are provided to illustrate the effectiveness of the proposed methodology for improvement of the quality of products.