Design Optimality Criteria of Reduced Models for Variations of Central Composite Design

Main Article Content

J. C. Nwanya
H. I. Mbachu
K. C. N. Dozie

Abstract

Choosing a response surface design to fit certain kinds of models is a difficult task. This work focuses on the reduced second order models having no quadratic and  no interaction terms for five variations of Central Composite Design (SCCD, RCCD, OCCD, Slope-R and FCC) using the D-, G- and A- optimality criteria. Results show that for models having no quadratic terms that G- and A-optimality criteria are equivalent and replication of the axial portion with increase in center points tends to decrease the D-, A- and G-optimality criteria values of the CCDs while for models having no interaction terms, replication of the axial portion with increase in center points increases the D-optimality criterion values of SCCD, RCCD and OCCD in all the factors considered. Finally, the work have shown that replication of the axial portion reduces the performance of the CCDs with models having no quadratic terms and Slope-R is a better design with respect to D- and A-optimality criteria.

Keywords:
CCDs, FDS, SCCD, RCCD, OCCD, Slope-R, FCC.

Article Details

How to Cite
C. Nwanya, J., I. Mbachu, H., & C. N. Dozie, K. (2020). Design Optimality Criteria of Reduced Models for Variations of Central Composite Design. Archives of Current Research International, 19(4), 1-7. https://doi.org/10.9734/acri/2019/v19i430164
Section
Original Research Article

References

Box GEP, Draper NR. The choice of a second order rotatable design. Biometrika. 1963;50:352–335.

Karson MJ, Manson AR, Hader RJ. Minimum bias estimation and experimental designs for response surfaces. Technometrics. 1969;11:475-461.

Chipman HA. Bayesian variable selection with related predictors. The Canadian Journal of Statistics. 1996;24:36-17.

Li C, Nachtsheim CJ. Model robust factorial designs. Technometrics. 2000;42: 352-345.

Borkowski JJ, Valeroso ES. Comparison of design optimality criteria of reduced models for response surface designs in the hypercube. Technometrics. 2001;43:477-468.

Chomtee B, Borkowski JJ. Comparison of response surface designs in spherical region. World Academy of Science, Engineering and Technology. 2012;65:4-1.

Yakubu Y, Chukwu AU. Comparison of optimality criteria of reduced models for response surface designs with restricted randomization. Progress in Applied Mathematics. 2012;4:126-110 .

Iwundu MP, Jaja EI. Precision of full polynomial response surface designs on models with missing coefficients. International Journal of Advanced Statistics and Probability. 2017;5(1):36-32.

Oyejola BA, Nwanya JC. Selecting the right central composite design. International Journal of Statistics and Application. 2015;5(1):30-21.

Onyeneke CC, Effanga EO. Application of reduced second order response surface model of convex optimization in paper producing industries. International Journal of Theoretical and Applied Mathematics. 2016;2(1):23-13.