An Evaluation of Practical Central Composite Designs for Optimum Exploration of Response Surfaces

Abstract

The drawback of the spherical, α=√k, and rotatable, α=∜f, f=2^k axial distances of the central composite designs (CCD) is the extreme values of the axial distance as the number of experimental factors, k, increases, resulting in impractical axial distances beyond the bounds of the design region. The practical central composite design compensates for this drawback by providing more stable and less extreme axial distance irrespective of the size of k. This study focuses on the evaluation of partially replicated cube and star portions of the variations of the CCD with practical axial distance, α=∜k. By replicating the cube and star portions. The variation of the partially replicated central composite designs was evaluated using the following single-value optimality criteria: A-, D- and E-efficiencies and V-criterion. Fraction of design space graphs (FDSG) and variance dispersion graphs (VDG) were used to assess the scaled and unscaled prediction variances across the design regions. The replication of the star points yielded small and better distribution of the prediction variance across the design space and better results for the A-, G- and V-criterion.. On the contrary, The D-efficiency was not improved by the replication of the cube portion. Lack-of-fit, residual and pure error degrees of freedom of partially replicated CCD were ascertained.