Abstract

<p>Efficiency and optimal properties of four varieties of Central Composite Design, namely, SCCD, RCCD, OCCD and FCCD and having ???????? replicates of the Fractional Factorial portion, ???????? replicates of the axial portion and ???????? replicates of the center portion are studied in four to six design variables. Optimal combination,[????????: ????????: ????????] of design points associated with the three portions of each central composite designs is presented. For SCCD, the optimal combinations resulting in A, D and G-efficient designs generally put emphasis on replicating the center portion of the SCCD. For RCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the factorial and center portions of the RCCD. However, with fixed factorial, axial and center portions, G-optimal and efficient designs are attained except for 26-2 design where emphasis is placed on replicating the factorial, axial and the center portions. For OCCD, the optimal combinations resulting in A- optimal and efficient designs generally put emphasis on replicating center portion of the OCCD. The optimal combinations resulting in D- optimal and efficient designs generally put emphasis on replicating the factorial and center portions of the OCCD. To achieve designs that are G-optimal and G-efficient, the optimal combination of design points generally put emphasis on replicating the factorial and the axial portions of the OCCD. For FCCD, the optimal combinations of design points resulting in Aoptimal and A-efficient designs put emphasis on replicating the axial portion of the FCCD. The optimal combinations resulting in D- optimal and efficient designs as well as G-optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the FCCD. It is interesting to note that for RCCD in 24-1 and 25-1 design variables, any ???? ????ℎ complete replicate of the distinct design points of the combination [????????: ????????: ????????] resulted in a G-efficient design. A super-efficient design having efficiency values greater than 100% emerged under the Dcriterion with A and G-efficiency values of 61.91% and 96.49%, respectively indicating that the design performed very well under such combinations as none of the values fell below 50%.</p>