On comparing the prediction variances of some central composite designs in spherical regions: a review

Chigbu, Polycarp E.; Ukaegbu, Eugene C.; Nwanya, Julius C.

doi:10.6092/issn.1973-2201/3560

Cited by 3 publications

(1 citation statement)

References 11 publications

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“…Many authors have studied the prediction variance properties of some second-order designs. Take for instance Borkowski [15] studied the scaled prediction variance of central composite designs (CCDs) and Box-Benhken designs (BBDs); Wesley et al [22] studied the prediction variance properties of split-plot designs in both the spherical and cuboidal region; Borkowski [12] studied the prediction variance capabilities of CCDs and BBDs in the spherical region; Chigbu et al [23] studied the prediction variance properties of some composite designs in the spherical region; Onwuamaeze [24] investigated the prediction variance properties of several cuboidal designs. ; Zahran et al [17] used the FDS graphs to assess the prediction capability of some designs; Oyejola and Nwanya [13] studied the prediction capability of inscribed central composite designs, by using FDS graphs; Nwanya and Dozie [14] used FDS graph to assess the prediction capability of some designs.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Oladugba¹,

Yankam²

2022

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Optimal Partially Replicated Cube, Star and Center Runs in Face-centered Central Composite Designs

Iwundu¹

2015

IJSP

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The variations of the Face-centered Central Composite Design under partial replications of design points are studied. The experimental conditions include replicating the cube points while the star points and center point are held fixed or not replicated, replicating the star points while the cube points and the center point are held fixed or not replicated and replicating the center point while the cube points and the star points are held fixed or not replicated. As a measure of goodness of the designs, D-and G-efficiency criteria are utilized. Results show that for the two-and three-variable quadratic models considered, the Face-centered Central Composite Design comprising of two cube portions, one star portion and a center point performed better than other variations under D-optimality criterion as well as G-optimality criterion. When compared with the traditional method of replicating the center point, the two cube portions, one star portion and a center point variation was relatively better in terms of design efficiency.

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Alternative Second-Order N-Point Spherical Response Surface Methodology Design and Their Efficiencies

Iwundu

2016

IJSP

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The equiradial designs are studied as alternative second-order N-point spherical Response Surface Methodology designs in two variables, for design radius ρ = 1.0. These designs are seen comparable with the standard second-order response surface methodology designs, namely the Central Composite Designs. The D-efficiencies of the equiradial designs are evaluated with respect to the spherical Central Composite Designs. Furthermore, D-efficiencies of the equiradial designs are evaluated with respect to the D-optimal exact designs defined on the design regions of the Circumscribed Central Composite Design, the Inscribed Central Composite Design and the Face-centered Central Composite Design. The D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the Inscribed Central Composite Design though inferior to the Circumscribed Central Composite Design with efficiency values less than 50% in all cases studied. Also, D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the N-point D-optimal exact designs defined on the design region supported by the design points of the Inscribed Central Composite Design. However, the N-point spherical equiradial designs are inferior to the N-point D-optimal exact designs defined on the design region supported by the design points of the Circumscribed Central Composite Design and those of the Face-centered Central Composite Design, with worse cases with respect to the design region of the Circumscribed Central Composite Design.

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On comparing the prediction variances of some central composite designs in spherical regions: a review

Cited by 3 publications

References 11 publications

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

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

Optimal Partially Replicated Cube, Star and Center Runs in Face-centered Central Composite Designs

Alternative Second-Order N-Point Spherical Response Surface Methodology Design and Their Efficiencies

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