Construction Of Optimal Second - Order Rotatable Central Composite Designs Through Resolutions With Application To Whiteness Of Cotton

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.