On Optimal Complete Replicated Rotatable, Orthogonal, Efficient and Relative Efficient Central Composite Designs

Abstract

Replication is the repetition of the treatments under investigation to different experimental unit. Replication is essential for obtaining a valid estimate of the experimental error and to a greater extent, increasing the precision of estimating the pairwise difference among the treatment effects. It is on this note that when full replication (replication of cube and star point) is made, there exists need for optimal replication for the purpose of minimizing biasedness. Some variations of experimental points of central composite designs in the presence of complete replication are compared under rotatable and orthogonal design restrictions. The optimal choice of the points replicated is obtained using the A-, D- and E- optimality criteria. Comparisons of the variations are given together with efficiency and the results suggest that replicated cubes plus replicated star points is better than partial replication of cube and star points under the design restrictions of rotatability and orthogonality.