Construction of Alternative Axial Points Using Standard Axial Points of Central Composite Design
Keywords:
Axial points, Optimality Criteria, Factorial points, Response Surface, Central composite designAbstract
There has been an over-flogged attention given to propositions on how one can make good choice of the existing axial points rather than procedural techniques for constructing axial points about the existing axial points. In order to curb this oversight, this work has constructed axial points about the standard axial points. The construction has given rise to * = 0.99k (where k is the number of factors) in comparison to the standard axial points = (where f is the number of factorial points). Both axial points have been implemented on a central composite design used for maximizing a four-factor process. The constructed axial points produced yields of about 87.211%, better than the yield of 87.187% produced by the standard axial points. Furthermore, the central composite design resulting from the constructed axial points satisfied the D-, A- and E-optimality criteria in comparison to that obtained from the standard or existing axial points.
References
A. Andrew. “Statistical details: Design selection”. Journal of Scientific Findings, vol. 14(3), pp.1-30, 2015.
G. E. P. Box & K. P. Wilson. “Response surface methodology”. Journal Storage, vol. 3(5), pp. 256-263, 1951.
M. Cavazzuh. “Optimization methods: From theory to design”. Springer-Verlag Berlin Heidelberg Journal, vol.2(3), pp. 13-43, 2013.
A. I. Khuri & J. A. Cornell. Response Surfaces, design and analysis. 2nd edition, Marcel Dekker Inc, Newyork, 1996
I. A. Khuri & S. Mukhopahyay. “Response surface methodology. Wiley Interdisciplinary Reviews”. Computational Statistics, vol.2(2), pp.128-149, 2010.
D. C. Montgomery. Response surface methodology: Design and Analysis of Experiments. USA: Wiley & Sons, 1995, pp. 246-298.
D. C. Montgomery. Response surface methodology: Design and Analysis of Experiments. USA: Wiley & Sons, 2013, pp. 478-553.
R. H. Myers, D. C. Montgomery and C. M. Anderson-Cook. Response Surface Methodology: Process and Product optimization using designed experiments. USA: 3rd edition Wiley, NY, 2009.
T. A. Ugbe, S. S. Akpan & J. E. Usen. “Reduction of Syrup Loss Owing to Frothing in Soft Drinks using Response Surface Methodology.” Global Journal of Mathematics, vol. 9(1), pp.663-672, 2017.
T. A. Ugbe, S. S. Akpan, U. J. Umondak, I. J. Udoeka & A. O. Ofem. “Response Surface Methodology and its Improvement in the Yield of Pineapple Fruit Drinks.”International Journal of Scientific & Engineering Research, vol.7(1), pp. 541-552, 2016.
J. E. Usen, S. S. Akpan, T. A. Ugbe, I. N. Ikpang, J. O. Uket and B. O. Obeten.“Multivariate-Based Technique for Solving Multi-Response Surface Optimization (MRSO) Problems: The Case of a Maximization Problem”. Asian Journal of Probability and Statistics, vol. 11(4), pp. 60-85, 2021.
J. E. Usen, E. J. Okoi, E. M. Egomo, E. N. Henshaw & B. E. Hogan. “A Critique on the Foundational Response Surface Methodology for Exploring Optimal Regions.” Asian Journal of Probability and Statistics, vol.8(2), pp.1-16, 2020.
C. F.J. Wu & D. Yuan. “Construction of response surface designs for qualitative and quantitative factors.” Journal of Statistical Planning and Inference, vol. 71(2), pp. 331-348, 1998.
Downloads
Published
How to Cite
Issue
Section
License
Authors who submit papers with this journal agree to the following terms.