Journal of Data Science

Abstract: Central composite design (CCD) is widely applied in many fields to construct a second-order response surface model with quantitative factors to help to increase the precision of the estimated model. When an experiment also includes qualitative factors, the effects between the quantitative and qualitative factors should be taken into consideration. In the present paper, D-optimal designs are investigated for models where the qualitative factors interact with, respectively, the linear effects, or the linear effects and 2-factor interactions or quadratic effects of the quantitative factors. It is shown that, at each qualitative level, the corresponding D-optimal design also consists of three portions as CCD, i.e. the cube design, the axial design and center points, but with different weights. An example about a chemical study is used to demonstrate how the D-optimal design obtained here may help to design an experiment with both quantitative and qualitative factors more efficiently.