D-optimal experimental design for production models in nonstandard experiments

Robust design is an effective Quality by Design method to reduce product variation by selecting levels of design factors. For a number of situations, a nonstandard design region with linearly limited resources is needed to conduct an experiment. In the literature, little attention has been given to the development of robust design models for the nonstandard design region with a combination of linearly limited resources and a limited number of design points. In this paper, a selection scheme of D-optimal experimental design points is proposed to generate design points using the modified exchange algorithm for the nonstandard design region while specifying linearly limited resources and the limited number of design points. The modified exchange algorithm is able to generate global design points with less time complexity than the improved Fedorov algorithm. In addition, robust design models linking a D-optimal experimental design with quality considerations are proposed in order to obtain optimum settings of design factors for the product. Comparative studies are also presented. Finally, a real-life experimental study shows that the proposed models with the desirability function and the sequential quadratic programming technique achieve greater variance reduction than the traditional counterparts.