On E–Optimality Design for Quadratic Response Surface Model

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Ukeme Paulinus Akra 1,* Edet Effiong Bassey 2 Ofong Edet Ntekim 3

1. Department of Statistics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin, Nigeria

2. Department of Mathematics, University of Calabar, Calabar, Nigeria

3. Department of Statistics, University of Calabar, Calabar, Nigeria

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2024.02.02

Received: 6 Feb. 2024 / Revised: 8 Mar. 2024 / Accepted: 5 Apr. 2024 / Published: 8 Jun. 2024

Index Terms

Optimal design, Response surface, E – Optimality and Quadratic response surface


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.

Cite This Paper

Ukeme Paulinus Akra, Edet Effiong Bassey, Ofong Edet Ntekim, "On E–Optimality Design for Quadratic Response Surface Model", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.10, No.2, pp. 13-22, 2024. DOI: 10.5815/ijmsc.2024.02.02


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