ON A – OPTIMILITY DESIGN FOR SOLVING SECOND - ORDER RESPONSE SURFACE DESIGN PROBLEMS
Abstract
Optimality criteria is a mechanism used for measuring the betterment of a design. Several traditional optimality criteria such as A, D, E, T, IV, etc, are the classes of optimal criterion for the test of optimum design. A – Optimality criterion as one of the traditional alphabetical criterion is used to examine the right selection of a design using second – order response surface models. In this paper, an algorithm and flowchart in line with a program to solve A – optimal design problem using second – order response surface model are developed. This paper also aimed to juxtaposing the accuracy between the manual and the programming technique in solving A – optimal problem. A six points of two designs with two explanatory variables were formulated to test the two methods. The result shows that the programming technique outperformed better than the manual method and it also minimizes error.
References
Akpan, S. S., and Akra, U. P. (2017). On exploration of first and second order response surface design model to obtain rotatability in a generalized case. Global Journal of Mathematics, vol.10 no.1, pp. 648 655.
Akpan, S., U. Akra, B. Asuquo and I. Udoeka (2017). On a new Lp Class to establish the relationship between various optimality criteria. Global Journal of Mathematics, vol. 10, no.2, pp.656 -664.
Akra, U. P., and Edet, E. B. (2017). Confounding 2k Factorial Design to Obtain Optimal yields using Different Organic Manure. Journal of Scientific and Engineering Research, 4(11);75-85.
Akra, U. P., E. E. Bassey., and O. E. Ntekim (2024). On EOptimality Design for Quadratic Response Surface Model. International Journal of Mathematical Sciences and Computing (IJMSC), 10(2); 13-22. https://doi.org/10.5815/ijmsc.2024.02.02 DOI: https://doi.org/10.5815/ijmsc.2024.02.02
Dieter, G. E., and Schmidt, L. C. (2009). Engineering design. Mcgraw-Hill, Boston. ISBN: 9780071271899.
Eric, N., and Kwabena, D. A. (2022). Approximate and Exact Optimal Designs for Paired Comparison Experiments. Calcutta Statistical Association Bulletin, vol.74, no.1, pp. 4258. DOI: https://doi.org/10.1177/00080683221079965
Holger, D., and Yuri, G. (2014). E-Optimal Designs for Second-order Response Surface Models. The Annals of statistics, vol.42, no.4, pp.16351656. DOI: https://doi.org/10.1214/14-AOS1241
Jasbir, A. S. (2012). Introduction to Optimum Design (Third Edition). University of Iowa, College of Engineering, Iowa City, Iowa. Pp 95 187.
Jones, B., and Nachtsheim, C. A. (2011). A class of three-level designs for definitive screening in the presence of second-order effects. Journal of Quality Technology, vol.43, no.1, pp. 115. DOI: https://doi.org/10.1080/00224065.2011.11917841
Magnusdottir, B. T. (2013). C-optimal designs for the bivariate Emax model, in mODa 10Advances in Model-Oriented Design and Analysis. Springer, pp. 153161. DOI: https://doi.org/10.1007/978-3-319-00218-7_18
Magnusdottir, B. T. (2016). Optimal designs for a multiresponse Emax model and efficient parameter estimation. Biometrical Journal, vol.58, no.3, pp.518534. DOI: https://doi.org/10.1002/bimj.201400203
Magnusdottir, B. T., and Nyquist, H. (2015). Simultaneous estimation of parameters in the bivariate Emax model. Statistics in medicine, vol.34, no.28, pp.37143723. DOI: https://doi.org/10.1002/sim.6585
Montgomery, D. C. (2013). Design and analysis of experiments, Volume 8, New York, John Wiley & Sons.
Myers,R. H.,D. C Montgomery and C. M Anderson-Cook. (2009). Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd ed. Wiley, Hoboken, New York.
Renata, E. T. (2021). Optimal design for dose-finding studies. P.hD dissertation in Statistics at Stockholm University, Sweden.
Schorning, K., H. Dette, K. Kettelhake, W. K. Wong and F. Bretz (2017). Optimal designs for active controlled dose-finding trials with efficacy-toxicity outcomes. Biometrika, vol.104, no.4, pp.10031010. DOI: https://doi.org/10.1093/biomet/asx057
Victorbabu, B., and Surekha, V. S. (2013). A note on measure of rotatability for Second order response surface designs using incomplete block designs.Journal of Statistics: Advances in Theory and Applications, vol.10, no.1, pp. 137-151.
Copyright (c) 2025 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
