The Impact of Increasing Centre Points on Three-Factor
Spherical N-Point Design Using Full Quadratic Model

Inamete Emem Ndah H.; Onu Obineke Henry; Hosea Yakubu

doi:https://doi.org/10.56201/ijcsmt.v8.no2.2022.pg17.31

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The Impact of Increasing Centre Points on Three-Factor Spherical N-Point Design Using Full Quadratic Model

Inamete Emem Ndah H., Onu Obineke Henry & Hosea Yakubu

Abstract

The study considered the Impact of increasing center points on three-factor spherical N-point Designs using quadratic model. The research considered how the increase in center points will affect the D-optimality, Sum of square errors, Grand Means of the designs as well as the Akaike information and Schwarz’ Bayesian Criteria. The center point’s addition considered were 1-5 inclusive. It was found that the D-optimality of the designs were maximized at 1 center point with the central composite circumscribed design (CCCD) having the highest value. This shows that the CCCD is the best three factor design on the basis of D-optimalty. The study shows that the Box-Behnken design (BBD) has the smallest sum of square error from 1 to 3 center points, while from 4 to 5 center points the CCCD recoreded the smallest sum of square error. The grand mean of Doehlert design and Central composite inscribed design increases for increasing center poins, while BBD decreases from 1 to 4 center points. The CCCD proves to be the best design based on AIC and SBC criteria, followed by CCID

Keywords

Three-factor designBox Behnken designDoehlert design and Central Composite design

References

Anup, K. D., & Saiket, D. (2018). Optimization of Extraction using Mathematical Models and Computation. Brandley, N. (2009). The Response Surface Methodology, a thesis proposal in the department of Mathematical Science, Indiana University of South Bend. Frits, B. S., & David, C. M., (2018). 13 th international Symposium on process systems Engineering. Iwundu, M. P. (2016a). Alternative Second-Order N-Point Spherical Response Surface Methodology Designs and Their Efficiencies. International Journal of Statistics and Probability; 5(4), 22-30. Iwundu, M.P. and Onu O.H. (2017). Preferences of equiradial designs with changing axial distances, design sizes and increase centre points and their relationship to the N-point central composite design: International journal of advanced statistics and probability, 5 (2), 77-82. Khuri, A. I. and Cornel, J. A. (1996). Response Surface: Design and Analysis. Second Edition. Marcel Dekker, Inc. New York. Oyejola, B. A., &Nwanya, J. C. (2015). Selecting the right Central Composite Design. Journal of Statistics and Applications, 5(1), 21-30. Magangi O. J. (2018). Construction of modified optimal second order rotatable designs Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2007).Response Surface Methodology: Process and Product Optimization using designed experiments. 3rd Edition.John Wiley & Sons, Inc. New Jersey. Nitin, V. &Vivek, K. (2019).Application of Box-Behnken Design for the optimization of cellulase production under solid-state fermentation.Springer Link.1(1733). Robert, W. M., (2009). New Box-Behnken Design, Knoxville, TN 37996-0532, U.S.A. Satriani, A. P., Rusli, D., Mohamad, Y. M. & OsmanH. (2013).Application of Box-Behnken Design in optimization of Glucose production from Oil Palm Empty Fruit Bunch Cellulose.International Journal of Polymer Science. Sergio, L. C., Walter, N. L., Cristina, M. Q., Benicio, B. N, & Juan, M. B. (2004).DoehlertMatrix:achemometric tool for analytical chemistry –review. Talanta 63(4),1061-1067. Shruti, S. R., & Padma, T., (2017).Selection of a design for response surface School of Biosciences and Technology, Vellore Institute of TechnologyVellore-632014, India. Suliman, R. (2017). Response Surface Methodology and Its Application in Optimizing the Efficiency of Organic Solar Cells, university Open PRAIRIE: Open Public Research Access Institutional Repository and Information Exchange. Verdooren, (2017).Use of Doehlert Designs for Second-order Polynomial Models.Springer Nature, 5 (2), 62-67. Wagna, P. C., Diogenes, R. G., Alete, P. T., Antonio, C. S., &Coata, M. G. (2008). Use of Doehlert design for optimizing the digestion of beans formulti-element determination by inductively coupled plasma optical emission spectrometry. Journal of the Brazilian chemical society, 19(1). Wardrop, D. M. (1985).Optimality criteria applied to certain response surface designs. William G. W. & Alain F., (2018).Cell Culture media in Bio Processing. Xiaoxia, P., Guang, Y., &Shanshan, L. (2020). Box-Behnken design based Statistical modeling for the extraction and Physicochemical properties of Pectin from Sunflower heads and the Comparison with commercial low-methoxyl Pectin. Scientific reports, 10(3595).

The Impact of Increasing Centre Points on Three-Factor Spherical N-Point Design Using Full Quadratic Model

Abstract

Keywords

References

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