Abstract
The equiradial designs are studied as alternative second-order N-point spherical Response Surface Methodology designs in two variables, for design radius ρ = 1.0. These designs are seen comparable with the standard second-order response surface methodology designs, namely the Central Composite Designs. The D-efficiencies of the equiradial designs are evaluated with respect to the spherical Central Composite Designs. Furthermore, D-efficiencies of the equiradial designs are evaluated with respect to the D-optimal exact designs defined on the design regions of the Circumscribed Central Composite Design, the Inscribed Central Composite Design and the Face-centered Central Composite Design. The D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the Inscribed Central Composite Design though inferior to the Circumscribed Central Composite Design with efficiency values less than 50% in all cases studied. Also, D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the N-point D-optimal exact designs defined on the design region supported by the design points of the Inscribed Central Composite Design. However, the N-point spherical equiradial designs are inferior to the N-point D-optimal exact designs defined on the design region supported by the design points of the Circumscribed Central Composite Design and those of the Face-centered Central Composite Design, with worse cases with respect to the design region of the Circumscribed Central Composite Design.
Highlights
Central Composite Designs (CCDs) play a vital role in modelling second-order response functions in the presence of curvature
D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the N-point D-optimal exact designs defined on the design region supported by the design points of the Inscribed Central Composite Design
The N-point spherical equiradial designs are inferior to the N-point D-optimal exact designs defined on the design region supported by the design points of the Circumscribed Central Composite Design and those of the Face-centered Central Composite Design, with worse cases with respect to the design region of the Circumscribed Central Composite Design
Summary
Central Composite Designs (CCDs) play a vital role in modelling second-order response functions in the presence of curvature. (2009) compared the prediction variances of some Central Composite Designs in spherical regions with radius α = √k where k is the number of model controllable variables. For the second order polynomial model used, results showed that the D-optimal designs defined over the rotatable Circumscribed Central Composite Design region had better determinant values than those defined over the Face-centered Central Composite Design region and the Inscribed Central Composite Design region. Iwundu (2015) studied the optimal partially replicated cube, star and center runs on design region supported by points of the Face-centered Central Composite Design, using quadratic models. X is the Nxp design matrix β is the px vector of unknown model parameters which are estimated on the basis of N uncorrelated observations. ε is the random additive error associated with Y and is independently and identically distributed with zero mean and constant variance
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