Mathematics and Statistics Vol. 9(5), pp. 760 - 772
DOI: 10.13189/ms.2021.090516
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Prediction Variance Capabilities of Third-Order Response Surface Designs for Cuboidal Regions

Brenda Mbouamba Yankam ^1,2,*, Abimibola Victoria Oladugba ^2
1 Cameroon Baptist Convention Health Services (CBCHS), Littoral Region, Cameroon
² Department of Statistics, University of Nigeria, Nsukka, Nigeria

ABSTRACT

Experimenters often evaluate the steadiness and consistency of designs over the region of interest by means of the prediction variance capabilities using the variance dispersion graph and the fraction of design space graph. The variance dispersion graph and the fraction of design space graph effectively describe the prediction variance capabilities of a design in the region of interest. However, the prediction variance capabilities of third-order response surface designs have not been studied in the literature. In this paper, the prediction variance capabilities of two third-order response surface designs term augmented orthogonal uniform composite designs and orthogonal array composite designs in the cuboidal region for 3≤k≤7 with center points are examined. The prediction variance capabilities are evaluated using the variance dispersion graph and the fraction of design space graph. Also, D-, E-, G-and T-optimality criteria are used in evaluating these designs in terms of single-value criterion. The results obtained show that the augmented orthogonal uniform composite designs have better prediction variance capabilities in the cuboidal region in the terms of the variance dispersion graphs for factors 3 and 4. The augmented orthogonal uniform composite designs also have better prediction variance capabilities for 3≤k≤7 compare to the orthogonal array composite designs in terms of the fraction of design space graph. The augmented orthogonal uniform composite designs are shown to be superior over the orthogonal array composite designs in terms of D-, E-, G-and T-optimality criteria for single-value criterion. This shows that the performances of the prediction variance capabilities of third-order response surface designs can be clearly visualized by means of the variance dispersion graph and fraction of design space and should be consider over the single-value criteria even though the single value-criteria show some degree of design performance. The augmented orthogonal uniform composite design is should often be considered in experimentation over the orthogonal array composite design since the augmented orthogonal uniform composite design performance better.

KEYWORDS
Response Surface Designs, Prediction Variance, Third-order Designs, Optimality Criteria, Variance Dispersion Graph, Fraction of Design Space Plot

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Brenda Mbouamba Yankam , Abimibola Victoria Oladugba , "Prediction Variance Capabilities of Third-Order Response Surface Designs for Cuboidal Regions," Mathematics and Statistics, Vol. 9, No. 5, pp. 760 - 772, 2021. DOI: 10.13189/ms.2021.090516.

(b). APA Format:
Brenda Mbouamba Yankam , Abimibola Victoria Oladugba (2021). Prediction Variance Capabilities of Third-Order Response Surface Designs for Cuboidal Regions. Mathematics and Statistics, 9(5), 760 - 772. DOI: 10.13189/ms.2021.090516.