Imposing D-optimality criterion on the design regions of the Central Composite Designs (CCD)

Abstract

The effect of D-optimality criterion in the construction of N-point exact designs on the design regions of the face-centered central composite design, rotatable (circumscribed) central composite design and inscribed central composite design, respectively, is investigated using a second order response surface model. Each geometric region has a finite number of support points defined by the factorial points, the axial points and the center point of the three central composite design regions. For the six parameter second order polynomial model used, the D-optimal design defined over the rotatable (circumscribed) Central Composite Design (CCD) region has better determinant values than those obtained over the face-centered central composite design region and the inscribed central composite design region. Furthermore, results indicate that D-optimal designs defined over the rotatable CCD region give better parameter estimates as the variances and covariances of the parameters are minimized.

Keywords: D-optimality criterion, face-centered CCD, inscribed CCD, circumscribed CCD