The Partial Replications of the Central Composite Designs for Spherical Regions

Authors

  • Francis Eze Department of Statistics Nnamdi-Azikiwe University, Awka Nigeria
  • F.C Eze Department of Statistics, Nnamdi-Azikiwe University, Awka, Nigeria

Keywords:

Fraction Design Space Graph, Axial Distances, Star points, Central Composite Design

Abstract

 Effects of partial replications of the star portion of the Central Composite Design (CCD) on the alternative axial distances were evaluated by comparing the performances of the replicated variations of the CCD in the spherical regions. The fractions of design space graphs (FDSG) of the star-replicated CCDs in the spherical region were plotted as well as the variance dispersion graph (VDG). The replication of the star portion of the CCD improved the prediction variance characteristics of the variations of the CCD in the spherical design regions. 

Downloads

Download data is not yet available.

References

Borkowski, J. J. (1995). Spherical Prediction Properties of Central Composite and Box Behnken Designs, Technometrics,Vol. 37 ( 4), 399 - 410.

https://doi.org/10.1080/00401706.1995.10484373

Chigbu, P. E., Ukaegbu, E. C. & Nwanya, J. C. (2009). On Comparing the Prediction Variances of Some Central Composite Designs in Spherical Region: A Review, Statistica, anno LXIX, n.4, 285-298.

Chigbu, P. E. & Ohaegbulem, U. O. (2011). On the Preference of Replicating Factorial Runs to Axial Runs in Restricted Second-Order Designs, Journal of Applied Sciences, Vol. 11 (22), 3732 - 3737.

https://doi.org/10.3923/jas.2011.3732.3737

Draper, N. R. (1982). Centre Points in Second-Order Response Surface Designs, Technometrics, Vol. 24 (2), 127 - 133. https://doi.org/10.1080/00401706.1982.10487734

Dykstra, O. Jr. (1959). Partial Duplication of Factorial Experiments, Technometrics, Vol. 1 (1), 63 - 75. https://doi.org/10.1080/00401706.1959.10489849

Dykstra, O. Jr. (1960). Partial Duplication of Response Surface Designs, Technometrics, Vol. 2 (2), 185 195.

https://doi.org/10.1080/00401706.1960.10489893

Giovannitti-Jensen, A. & Myers, R.H. (1989). Graphical Assessment of the Prediction Capability of Response Surface Designs, Technometrics, Vol. 31 (2), 159 - 171.

https://doi.org/10.1080/00401706.1989.10488510

Li, J., Liang, L., Borror, C. M., Anderson-Cook, C. M. & Montgomery, D.C. (2009). Graphical Summaries to Compare Prediction Variance Performance for Variations of the Central Composite Design for 6 to 10 Factors, Quality Technology and Quantitative Management, Vol. 6 (4), 433 - 449. https://doi.org/10.1080/16843703.2009.11673209

Onyishi, L.I and Eze, F.C. (2020). Alternative Axial Distances for Spherical Regions of Central Composite Designs. Earthline Journal of Mathematical SciencesVolume 4, Number 2, pp 273-285 https://doi.org/10.34198/ejms.4220.273285

Onukogu, I. B. (1997). Foundations of Optimum Exploration of Response Surfaces, Ephrata Press, Nsukka.

Ozol-Godfrey, A., Anderson-Cook, C. M. & Montgomery, D. C. (2005). Fraction of Design Space Plots for Examining Model Robustness, Journal of Quality Technology, Vol. 37, 223 - 235.

https://doi.org/10.1080/00224065.2005.11980323

Ukaegbu, E. C. (2017). Evaluation of Prediction Capabilities of Partially Replicated Variations of Some Central Composite Design, A PhD Thesis Submitted to the Department of Statistics, University of Nigeria, Nsukka.

Ukaegbu, E. C. & Chigbu, P. E. (2015a). Characterization of Prediction Variance Properties of Rotatable Central Composite Designs for 3 to 10 Factors, International Journal of Computational & Theoretical Statistics, Vol. 2 (2), pp. 87 - 97.

https://doi.org/10.12785/ijcts/020203

[Ukaegbu, E. C. & Chigbu, P. E. (2015b). Graphical Evaluation of the Prediction Capabilities of Partially Replicated Orthogonal Central Composite Designs, Quality and Reliability Engineering International, Vol. 31, pp. 707 - 717, DOI: 10.1002/qre.1630.

https://doi.org/10.1002/qre.1630

Downloads

Published

2020-12-31

How to Cite

Eze, F., & Eze, F. (2020). The Partial Replications of the Central Composite Designs for Spherical Regions. MathLAB Journal, 7, 139-159. Retrieved from https://purkh.com/index.php/mathlab/article/view/863

Issue

Section

Research Articles

Most read articles by the same author(s)