On the Preference of Replicating Factorial Runs to Axial Runs in Restricted Second-order Designs

Chigbu, Polycarp E.; Ohaegbulem, Emmanuel U.

doi:10.3923/jas.2011.3732.3737

Cited by 7 publications

(4 citation statements)

References 1 publication

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“…It was shown from their result that the CCDs (CCCD, CCFD and CCID) are at their best when the G-efficiency is employed for all the factors considered while the CCID, in particular, behaves poorly when using the A-and D-efficiencies. Chigbu and Ohaegbulem (2011), in their study, applied the D-optimality criterion, which is a response Published by Al-Kindi Center for Research and Development. Copyright (c) the author(s).…”

Section:   mentioning

confidence: 99%

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Evaluating Percentage Rotatability For The Small Box – Behnken Design

Kiwu

Bartholomew

Kiwu-Lawrence

et al. 2021

jmss

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Rotatability property for the Small Box-Behnken design is discussed in this paper. This paper aimed at applying a measure of obtaining percentage rotatability on the Small Box-Behnken designs to determine if the Small Box-behnken designs are rotatable or not and investigated the extent of rotatability in terms of percentage. The factors, q, considered range from 3 to 11. The results showed that for factors q, the Small Box-Behnken design is rotatable for q = 3 factors, near rotatable for q = 4, 7 factors and not rotatable for q = 5, 6, 8, 9, 10 and 11 factors.

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Section:   mentioning

confidence: 99%

“…According toMontgomery (2005), the model in (2) of order r , with q factors If the factors are codes as in(6) and the model is fitted in a spherical region, we have the following representation,…”

mentioning

confidence: 99%

Evaluating Percentage Rotatability For The Small Box – Behnken Design

Kiwu

Bartholomew

Kiwu-Lawrence

et al. 2021

jmss

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“…Two variations of central composite designs under the orthogonal and rotatable restriction using the D optimality criterion were compared by Chigbu and Ohaegbulem (2011) and they concluded that the replicated cube plus one star variation is better than the replicated star plus one cube variation under both restrictions. as well as the D optimality and A optimality criteria.…”

Section: Introductionmentioning

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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“…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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On the Preference of Replicating Factorial Runs to Axial Runs in Restricted Second-order Designs

Cited by 7 publications

References 1 publication

Evaluating Percentage Rotatability For The Small Box – Behnken Design

Evaluating Percentage Rotatability For The Small Box – Behnken Design

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

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

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