The Effects of Addition of n_c Center Points on the Optimality of Box-Benhken and Box-Wilson Second-Order Designs

摘要

Relationships between optimal design properties and changing sizes of designs, by the addition of center points, are seen to be very strong between the Box-Benhken designs and the Box-Wilson designs defined at and Variations seem to exist with Box-Wilson designs defined at α = 1.0. In particular, the determinant values of the information matrices of the Box-Benhken designs generally decrease as increases. These are also true for all categories of the Box-Wilson designs. However, the minimum eigenvalue of the Box-Benhken design and the Box-Wilson design defined at and is maximized when and maximized when for the Box-Wilson design defined at α = 1.0. For the Box-Benhken designs considered, the trace values of the variance-covariance matrices generally decrease as increases. This is also true for the Box-Wilson designs defined at and For the Box-Wilson designs defined at α = 1.0, the trace values of the variance-covariance matrices increase as increases. The maximum scaled predictive variances associated with the Box-Benhken designs and the Box-Wilson designs generally increase as increases and minimized when for Box-Wilson design defined at and when for the Box-Benhken design and the Box-Wilson design defined at and The trace of information matrix associated with all considered design types consistently decreases as increases.