Asian Journal of Probability and Statistics

This study is a comparative study of four varieties of Central Composite Design (namely; FCCD, RCCD, SCCD, and OCCD) using D-, G-, and A- efficiencies under full-factorial design structures (k=2 to 10) and fractional-factorial design structures (k = 5 to 10) with the number of center points, n₀ 1 to 8). The results obtained showed varying performances. For full-factorial design structures, as the number of factors was increased, G-efficiencies were greater than the D- and A- efficiencies for k = 2 to 7 in FCCD, RCCD, and OCCD. For k = 8 to 10, the D-efficiencies were greater than the G- and A- efficiencies.  A- efficiencies were the lowest, except in SCCD, where they were greater than the D- efficiencies for the number of factors, k = 4 to 8. Also, as the number of center points was increased, the efficiencies were reducing in most cases. In FCCD, the D-, G-, and A- efficiencies decreased all through the number of factors, k = 2 to 10. In RCCD, for k = 2, 3, 4, and 6, the D-, G-, and A- efficiencies decreased; for k = 5, 7, and 9, the D- and G- efficiencies decreased, while the A-efficiencies increased; for k = 8, the D- and A- efficiencies decreased, while G-efficiency increased; for k=10, the D-efficiencies deceased, A-efficiencies increased, while the G-efficiencies appeared to be steady. In SCCD, for k=2, the D-, G-, and A- efficiencies decreased; for k = 3 to 6, the D- and G- efficiencies decreased, while A-efficiencies increased; for k=7, the D- and A- efficiencies increased, while the G-efficiencies decreased; for k=8 and 9, the G- and  A- efficiencies increased, while the D-efficiencies decreased, for k=10, the D-, G-, and A- efficiencies increased. In OCCD, the D- and A- efficiencies increased, while the G-efficiencies decreased for k = 2 to 6; for k=7, the D- and G- efficiencies increased, while the A-efficiencies decreased; for k=8, the D- and A- efficiencies gradually increased, while the G-efficiencies gradually decreased; for k=9 and 10, the D-, G-, and A- efficiencies increased. For the fractional-factorial design structures, G-efficiencies were greater than the D- and A- efficiencies for k = 5 to 7, but D-efficiencies became greater for k = 8 to 10 in FCCD, RCCD, and OCCD. In SCCD, D-efficiencies were greater than the G- and A- efficiencies for k = 5 and 10, while G-efficiencies were greater from k = 6 to 9. Also, as the number of center points was increased, the D-, G-, and A- efficiencies decreased in FCCD, RCCD, and SCCD for k = 5 to 9. For k = 10, A- and G- efficiencies increased, while D-efficiencies decreased; in OCCD the D- and G- efficiencies decreased, while the A-efficiencies increased for k = 5 to 8. For k = 9, the D- and A-efficiencies increased, while the G-efficiencies decreased. For k = 10, the D-, G-, and A- efficiencies gradually increased. In general, the study concluded that fractional-factorial design structures performed better than full-factorial design structures, particularly as the number of factors increased from k = 6 to 10). These findings re-emphasized the importance of considering both the number of factors and center points when selecting an experimental design.