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.
Highlights
The second-order response surface model is applied widespreadly in many research fields through the central composite design (CCD)
A chemical study of flue gas desulfurization published by Zainudin et al (2005), for illustration, deals with an adsorbent for removing the sulfur dioxide (SO2) in the flue gas
Qualitative and quantitative factors considered simultaneously in one experiment perplex the response surface designs if some quantitative effects of interest are varied at the qualitative levels
Summary
The second-order response surface model is applied widespreadly in many research fields through the central composite design (CCD). The experiment including a total of 40 runs with three quantitative factors and one 2-level qualitative factor was performed to fit a second-order response surface model. If the interactions between qualitative and quantitative factors are assumed to be negligible, one can express the quantitative effects under second-order regression model as. Qualitative and quantitative factors considered simultaneously in one experiment perplex the response surface designs if some quantitative effects of interest are varied at the qualitative levels. When there is no interaction between qualitative and quantitative factors, D-optimal design can be constructed as a product of those designs which are D-optimal in the corresponding single-factor models, see Schwabe and Wierich (1995). Other for estimating the interactions and quadratic effects; (ii) the design collapsed over the qualitative levels forms an efficient design for the second-order response surface design for quantitative factors.
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