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Assessment of composite mixed resolution designs in spherical regions


Cynthia N. Umegwuagu, Polycarp E. Chigbu and Eugene C. Ukaegbu

JOURNAL: Journal of Nigerian Statistical Association Vol.32, 2020
YEAR: 2020


Composite Mixed Resolution Designs (CMRD) were evaluated using some design assessment criteria: D- and G-efficiencies, I-optimality and Condition Number in spherical regions. The effect of centre points, as well as the effect of the replication of the cube and star portions of the designs, were also evaluated. The CMRDs achieved high G- and D-efficiencies with zero or one centre points and minimum I-optimality criterion with four centre points. Also, replication of the cube and star portions of the designs improved the I-optimality criterion but did not improve the D- and G-efficiencies and the Condition Number.


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

Borkowski, J.J. and Lucas, J.M. (1997). Designs of Mixed Resolution for Process Robustness Studies, Technometrics, 39, 63 - 70.

Borkowski, J.J. and Valeroso, E.S. (2001). Comparison of Design Optimality Criteria of Reduced Models for Response Surface Designs in the Hypercube, Technometrics, 43(4), 468 – 477.

Box, G.E.P. and Draper, N.R. (1963). The Choice of a Second Order Rotatable Design, Biometrika, 50(3/4), 335-352.

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

Draper, N.R. (1982). Centre Points in Second-Order Response Surface Designs, Technometrics, 24 (2), 127-133.

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

Fries, A. and Hunter, W.G. (1980). Minimum Aberration 2k-p Designs, Technometrics, 22, 601 - 608.

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

Hardin, R.H. and Sloane, N.J.A. (1993). A New Approach to the Construction of Optimal Designs, Journal of Statistical Planning and Inference, 37, 339-369.

Li, J., Liang, L., Borror, C.M., Anderson-Cook, C.M. and 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, 6(4), 433 - 449.

Leiviskä, K. 2013. Introduction to Experiment Design, Control Engineering Laboratory, University of Oulu, Finland.

Montgomery, D.C. (2013). Design and Analysis of Experiments, 8th edition, John Wiley & Sons, Hoboken, NJ.

Myers, R.H., Khuri A.I. and Vining G. (1992). Response Surface Alternatives to the Taguchi Robust Parameter Design Approach, The American Statistician, 46, 131 - 139.

Myers, R. H., Montgomery, D. C. and Anderson-Cook, C. M. 2009. Response Surface Methodology: Process and Product Optimization using Designed Experiments, 3rd edition, John Wiley & Sons, Inc., Hoboken, New Jersey.

Robinson, T.J. and Wulff, S.S. (2006). Response Surface Approaches to Robust Parameter Design, In: Response Surface Methodology and Related Topics by Khuri, A.I. (Editor), World Scientific Press, Singapore, 123 - 158.

Rady, E. A., El-Monsef, M.M.E. Abd and Seyam, M.M. (2009). Relationships among Several Optimality Criteria, InterStat: Statistics on the Internet, 6(1), 1 - 11.

Shoemaker, A.C., Tsui, K.L. and Wu, C.F.J. (1989). Economical Experimentation Methods for Robust Parameter Design, Paper presented at the Fall Technical Conference, American Society of Quality Control, Houston, TX.

Shoemaker, A.C., Tsui, K.L., and Wu, C.F.J. (1991). Economical Experimentation Methods for Robust Design, Technometrics, 33, 415 - 427.

Smith, K. (1918). On the Standard Deviations of Adjusted and Interpolated Values of an Observed Polynomial Function and it's Constant and The Guidance They Give Towards a Proper Choice of the Distribution of Observations, Biometrika, 12, 1–85.

Taguchi, G. and Wu, Y. (1980). Introduction to Off-Line Quality Control, Central Japan Quality Control Association (available from American Supplier Institute, 32100 Detroit Industrial Expressway, Romulus, MI 48174).

Ukaegbu, E.C. and Chigbu, P.E. (2015). Comparison of Prediction Capabilities of Partially Replicated Central Composite Designs in Cuboidal Region, Communications in Statistics- Theory and Methods, 44 (2), 406 – 427.

Wald, A. (1943). On the Efficient Design of Statistical Investigations, Annals of Mathematical Statistics, 14, 134–140.


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