Mathematics and Statistics Vol. 10(1), pp. 61 - 73
DOI: 10.13189/ms.2022.100105
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Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

Abimibola Victoria Oladugba , Brenda Mbouamba Yankam ^*
Department of Statistics, University of Nigeria, Nsukka, Nigeria

ABSTRACT

The variance dispersion graphs (VDGs) and the fraction of design space (FDS) graphs are two graphical methods that effectively describe and evaluate the points of best and worst prediction capability of a design using the scaled prediction variance properties. These graphs are often utilized as an alternative to the single-value criteria such as D- and E- when they fail to describe the true nature of designs. In this paper, the VDGs and FDS graphs of third-order orthogonal uniform composite designs (OUCD₄) and orthogonal array composite designs (OACD₄) using the scaled-prediction variance properties in the spherical region for 2 to 7 factors are studied throughout the design region and over a fraction of space. Single-valued criteria such as D-, A- and G-optimality are also studied. The results obtained show that the OUCD₄ is more optimal than the OACD₄ in terms of D-, A- and G-optimality. The OUCD₄ was shown to possess a more stable and uniform scaled-prediction variance throughout the design region and over a fraction of design space than the OACD₄ although the stability of both designs slightly deteriorated towards the extremes.

KEYWORDS
Scaled-Prediction Variance, Variance Dispersion Graphs, Fraction of Design Space Graphs Orthogonal Uniform Composite Designs, Spherical Region, G-Optimality Criterion

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Abimibola Victoria Oladugba , Brenda Mbouamba Yankam , "Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere," Mathematics and Statistics, Vol. 10, No. 1, pp. 61 - 73, 2022. DOI: 10.13189/ms.2022.100105.

(b). APA Format:
Abimibola Victoria Oladugba , Brenda Mbouamba Yankam (2022). Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere. Mathematics and Statistics, 10(1), 61 - 73. DOI: 10.13189/ms.2022.100105.