On The Optimal Choice of Cube and Star Replications in Restricted Second-Order Designs

Nduka, Uchenna Chinedu; Chigbu, Polycarp E.

doi:10.1080/03610926.2012.725499

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…Chigbu and Ohaegbulem (2011), compared two variations of central composite designs under the orthogonal and rotatable restriction using the D optimality criterion and concluded that the replicated cube plus one star variation is better than the replicated star plus one cube variation under both restrictions. Nduka and Chigbu (2014)…”

Section: Introductionmentioning

confidence: 99%

Some Optimality Variations of Central Composite Designs

Ngonadi¹,

Eze²

2019

AJAMS

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Some variations of central composite designs (CCD) under complete and partial replications of cube, axial and center points are studied using A, D and G optimality criteria. The results obtained suggest that complete replication of the cube, axial and center points are better than the partial replication of cube, axial and center points under the A and D optimality criteria studied while it varies under G optimality criterion. The partial replication of the cube, axial and center point for all the CCDs studied, the partial replicated cube point is D optimal but varies under A and G optimality criteria.

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Section: Introductionmentioning

confidence: 99%

Some Optimality Variations of Central Composite Designs

Ngonadi¹,

Eze²

2019

AJAMS

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“…For the preference of replicating the cube to star points of the ccd, we shall consider the following variations; see Nduka & Chigbu (2014) one cube plus two replicated stars, n α = 2 two replicated cubes plus one star, n F = 2 one cube plus three replicated stars, n α = 3 three replicated cubes plus one star, n F = 3 one cube plus four replicated stars, n α = 4 four replicated cubes plus one star, n F = 4…”

Section: Quantiles Of the Variations Of Partially Replicated Ccdmentioning

confidence: 99%

“…Often in design comparison, single value design optimality criteria are used, see, for example Lucas (1976). Chigbu and Ohaegbulam (2011) and Nduka and Chigbu (2014) compared two variations of the partially replicated orthogonal and rotatable ccd using D− optimality criteria and Schur ordering for 2 to 5 input variables. The variations are the replicated cube plus one star and the replicated star plus one cube.…”

Section: Introductionmentioning

confidence: 99%

Quantile Plots of the Prediction Variance for Partially Replicated Central Composite Design

Umelo-Ibemere¹,

Amuji²

2015

IJSP

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Sometimes, it is not feasible to fully replicate the experimental units. When this happen, there is need for optimal replication of the experimental units to avoid bias. The prediction variance of two variations of the partially replicated central composite design (replicated cube plus one star and one cube plus replicated star) are compared using the quantile plots. These plots provide information about the prediction variance distribution on a sphere for comprehensive evaluation of the quality of the prediction variance. For face-centred (α = 1) and rotatable (α = F 1 4 ) central composite designs, the prediction variance of the one cube plus replicated star perform better than the replicated cube plus one star. Unlike the replicated cube plus one star, the quantile plots of the scaled prediction variance of the one cube plus replicated star depict near rotatability.

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“…Nduka and Chigbu (2014) compared two variation of N point orthogonal and rotatable central Composite design based on Schur's ordering of design which says…”

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confidence: 99%

Design Efficiency and Optimal Values of Replicated Central Composite Designs with Full Factorial Portions

Iwundu¹,

Oko²

2021

African Journal of Mathematics and Statistics Studies

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Efficiency and optimal properties of four varieties of Central Composite Design, namely, SCCD, RCCD, OCCD and FCCD and having r_f replicates of the full factorial portion, r_α replicates of the axial portion and r_c replicates of the center portion are studied in four to six design variables. Optimal combination,[r_f: r_α: r_c ] of design points associated with the three portions of each central composite design is presented. For SCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the center portion of the SCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For RCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the factorial and center portions of the RCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For OCCD, the optimal combinations resulting in A- optimal and efficient designs generally put emphasis on replicating the axial and center portion of the OCCD. The optimal combinations resulting in G- optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the OCCD. To achieve designs that are D-optimal and D-efficient, the optimal combination of design points generally put emphasis on replicating the center portion of the OCCD. For FCCD, the optimal combinations of design points resulting in A-efficient designs put emphasis on replicating the axial portion of the FCCD. The optimal combinations resulting in G- optimal and efficient designs as well as G-optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the FCCD. It is interesting to note that for FCCD in five design variables, any r^th complete replicate of the distinct design points of the combination [r_f: r_α: r_c ] resulted in a D-efficient design. Many super-efficient designs having efficiency values greater than 1.0 emerged under the D-criterion. Unfortunately, these designs did not perform very well under A- and G-criteria, having some efficiency values much below 0.5 or just about 0.6.

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On The Optimal Choice of Cube and Star Replications in Restricted Second-Order Designs

Cited by 4 publications

References 7 publications

Some Optimality Variations of Central Composite Designs

Some Optimality Variations of Central Composite Designs

Quantile Plots of the Prediction Variance for Partially Replicated Central Composite Design

Design Efficiency and Optimal Values of Replicated Central Composite Designs with Full Factorial Portions

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