Prediction Variance Capabilities of Third-Order Response Surface Designs for Cuboidal Regions

Yankam, Brenda Mbouamba; Oladugba, Abimibola Victoria

doi:10.13189/ms.2021.090516

Cited by 1 publication

(3 citation statements)

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“…The orthogonal uniform composite design (OUCD 4 ) is a new third-order response surface design introduced by Yankam and Oladugba [9]. These OUCD 4 are good space-filling designs that are nearly rotatable and nearly orthogonal third-order response surface designs.…”

Section: Orthogonal Uniform Composite Designs (Oucd 4 )mentioning

confidence: 99%

“…Zhang et al [4] constructed third-order orthogonal array composite designs (OACD 4 ) to estimate the third-order model parameters. Yankam and Oladugba [9] constructed third-order orthogonal uniform composite designs (OUCD 4 ) to estimate the third-order model parameters. These designs are commonly selected using the best single-valued criteria, such as D-optimality, which considers the variance and covariances of the model's coefficient estimates, I-optimality, which considers the average variance for a projected value over the region of interest, and G-optimality, which considers the overall variance for a projected value over the region of interest [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the prediction variance properties of two third-order designs; orthogonal uniform composite designs (OUCD 4 ) introduced by Yankam and Oladugba [9] and orthogonal array composite designs (OACD 4 ) introduced by Zhang et al [4] using VDG and FDS graphs are studied. These designs have several advantages, including the ability to use resolution IV design for factor screening, the capacity to execute in-depth analysis, the ability to provide more flexible run sizes than other types of composite designs, and the ability to perform multiple analyses for cross-validation.…”

Section: Introductionmentioning

confidence: 99%

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Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

Oladugba¹,

Yankam²

2022

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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 (OUCD 4 ) and orthogonal array composite designs (OACD 4 ) 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 OUCD 4 is more optimal than the OACD 4 in terms of D-, A-and G-optimality. The OUCD 4 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 OACD 4 although the stability of both designs slightly deteriorated towards the extremes.

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Section: Orthogonal Uniform Composite Designs (Oucd 4 )mentioning

confidence: 99%