On E–Optimality Design for Quadratic Response Surface Model
Автор: Ukeme Paulinus Akra, Edet Effiong Bassey, Ofong Edet Ntekim
Журнал: International Journal of Mathematical Sciences and Computing @ijmsc
Статья в выпуске: 2 vol.10, 2024 года.
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In response surface methodology, optimality criteria is a major tools used to measure the goodness of a design. Optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. E – Optimality criterion is one of the traditional alphabetical criterion used to explore the right choice of a design in both linear and quadratic response surface models. In this paper, we investigated E – optimal experimental designs for a quadratic response surface model with two factor predictors. We developed an algorithm and a flowchart in line with a program to obtain E – optimal design and compare the result with an existing method. Two designs were formulated each with six points to illustrate the usefulness of the new method. The result revealed that the new technique outperformed better than the existing method. The significance of the later to the former technique is that, it minimizes error due to approximation and also make the computation of the aforementioned optimality easier. We, therefore recommended this method to be used at all length of points when E – optimality is to be evaluated.
Optimal design, Response surface, E – Optimality and Quadratic response surface
Короткий адрес: https://sciup.org/15019078
IDR: 15019078 | DOI: 10.5815/ijmsc.2024.02.02
Список литературы On E–Optimality Design for Quadratic Response Surface Model
- B. Jones and C. A. Nachtsheim. 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. 1–15, 2011.
- D. C. Montgomery. Design and analysis of experiments, Volume 8, New York, John Wiley & Sons, 2013.
- R. H. Myers, D. C. Montgomery and C. M. Anderson-Cook. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd ed. Wiley, Hoboken, New York, 2009
- B. Victorbabu and V. S. Surekha. 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, 2013.
- S. S. Akpan and U. P. Akra. 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, 2017.
- S. K. Padmanabhan, F. Hsuan and V. Dragalin. Adaptive penalized D-optimal designs for dose finding based on continuous efficacy and toxicity. Statistics in Biopharmaceutical Research, vol.2, no.2, pp.182– 198, 2010.
- B. T. Magnusdottir. C-optimal designs for the bivariate Emax model, in ‘mODa 10–Advances in Model-Oriented Design and Analysis. Springer, pp. 153–161, 2013.
- K. Schorning, H. Dette, K. Kettelhake, W. K. Wong and F. Bretz. Optimal designs for active controlled dose-finding trials with efficacy-toxicity outcomes. Biometrika, vol.104, no.4, pp.1003–1010, 2017.
- D. Holger and G. Yuri. E-Optimal Designs for Second-order Response Surface Models. The Annals of statistics, vol.42, no.4, pp.1635–1656, 2014.
- B. T. Magnusdottir and H. Nyquist. Simultaneous estimation of parameters in the bivariate Emax model. Statistics in medicine, vol.34, no.28, pp.3714–3723, 2015.
- B. T. Magnusdottir. Optimal designs for a multiresponse Emax model and efficient parameter estimation. Biometrical Journal, vol.58, no.3, pp.518–534, 2016.
- E. T. Renata. Optimal design for dose-finding studies. P.hD dissertation in Statistics at Stockholm University, Sweden, 2021
- S. Akpan, U. Akra, B. Asuquo and I. Udoeka. On a new Lp – Class to establish the relationship between various optimality criteria. Global Journal of Mathematics, vol. 10, no.2, pp.656 -664, 2017.
- N. Eric and D. A. Kwabena. Approximate and Exact Optimal Designs for Paired Comparison Experiments. Calcutta Statistical Association Bulletin, vol.74, no.1, pp. 42–58, 2022
- A. S. Jasbir. Introduction to Optimum Design (Third Edition). University of Iowa, College of Engineering, Iowa City, Iowa. Pp 95 – 187, 2012