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Alphabetic Optimality Criteria for 2 K Central Composite Design

Author

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  • Francis C. Eze*

    (Department of Statistics, Nnamdi-Azikiwe University, Awka, Anambra State, Nigeria)

  • Lilian Ngonadi O.

    (Department of Statistics, Nnamdi-Azikiwe University, Awka, Anambra State, Nigeria)

Abstract

Designing an appropriate central composite design involves selection of the right type of central composite design. The various Central composite designs(CCDs); Spherical central composite design (SCCD), Rotatable central composite design (RCCD), Orthogonal central composite design (OCCD) and Face centered cube design (FCCD) were compared for factors k =2 to 6 using the D, G and A criteria. The ? (axial) values were obtained for the various Central composite design (SCCD, RCCD, OCCD and FCD) and the values used to find relevant results for factors k=2 to 6. The efficiency values were obtained for the D, A and G optimality criteria in which larger values imply better design. The axial portion and cube portion were replicated with the center points increased one and three times. The results show that replicating the star points tends to reduce the D and G-optimality criteria of the CCDs (SCCD, RCCD, OCCD and FCCD) at some factor levels while it is different for the A optimality criterion. The results suggest replication affects the different criteria in very different ways because what improves one criterion may be detrimental to a different criterion. The overall results show that G optimality criteria performed better than D and A optimality in different factor levels and replications.

Suggested Citation

  • Francis C. Eze* & Lilian Ngonadi O., 2018. "Alphabetic Optimality Criteria for 2 K Central Composite Design," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 4(9), pages 107-118, 09-2018.
    • Handle: RePEc:arp:ajoams:2018:p:107-118
    DOI: arpgweb.com/?ic=journal&journal=17&info=aims
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    References listed on IDEAS

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    1. Polycarp E. Chigbu & Eugene C. Ukaegbu & Julius C. Nwanya, 2009. "On comparing the prediction variances of some central composite designs in spherical regions: a review," Statistica, Department of Statistics, University of Bologna, vol. 69(4), pages 286-298.
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