Abstract:
Resolution of a design refers to the degree to which estimated main effects are
confounded with estimated two or more than two-level interactions. Optimal designs
reduce the costs of experimentation by allowing statistical models to be estimated with
fewer experimental runs. The purpose of this study was to construct optimal rotatable
designs through resolutions as well as explore and optimize response surfaces. Rotatable
designs were constructed through resolutions III and IV for three and four factors based
on the Central Composite Designs. Information matrices based on the parameter
subsystem of interest on the second-degree Kronecker model were obtained. Optimal
rotatable Weighted Central Composite Designs were derived and optimality was
accomplished through application of D-, A- , E- and I-optimality criterion. A generalized
form of the constructed D- and I-optimal rotatable WCCDs for m factors was derived
together with the corresponding optimal values. The efficiency of the designs was also
determined over the full CCD. A CCD with four factors was used to illustrate the
practicability of the derived rotatable designs where optimal conditions for effects on
whiteness of cotton using Peracetic Acid in the presence of a Bleaching Agent were
obtained by locating the stationary points. Optimal whiteness index was obtained using
full CCD and resolution IV CCD and the efficiency of the latter was found to be 0.9678.
The derived rotatable designs were found to beD-, A-, E- and I- optimal as well as more
efficient than uniformly weighted CCDs. It was concluded that rotatable designs
constructed through resolution R and assigning different weights to the support points are
better. The experimental runs are reduced hence economical and the resulting designs are
improved in terms of optimality and estimation efficiency. The results also showed that
the D-optimal resolution III design gives more weight to the cube portion while
resolution IV design gives equal weight to both portions. But A- and I- optimal designs
assign greater weight to the star portion than the cube portion.
