Volume 4, Issue 2, April 2018, Page: 32-37
Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions
Dennis Matundura Mwan, Department of Statistics and Computer Science, School of Biological and Physical Science, Moi University, Eldoret, Kenya
Mathew Kosgei, Department of Statistics and Computer Science, School of Biological and Physical Science, Moi University, Eldoret, Kenya
Received: May 29, 2018;       Accepted: Jul. 6, 2018;       Published: Aug. 4, 2018
DOI: 10.11648/j.ijdsa.20180402.11      View  431      Downloads  23
Abstract
The theory of optimal experimental designs is concerned with the construction of designs that are optimum with respect to some statistical criteria. Some of these criteria include the alphabetic optimality criteria such as; D-, A-, E-, T-, G- and C- criterion. Compound optimality criteria are those that combine two or more alphabetic optimality criteria. Design that require optimality criteria have specific desired properties that do very well in one design and at the same time perform poorly in another design. Thus, a compound optimality criterion gives a balance to the desirability of any two or more alphabetic optimality criteria. The present paper aims to introduce CD- and DT- criteria which are compound optimality criteria for second order rotatable designs constructed using Balanced Incomplete Block Designs (BIBDs) in four dimensions.
Keywords
Optimality Criteria, Compound Criteria, DT-optimum and CD-optimum
To cite this article
Dennis Matundura Mwan, Mathew Kosgei, Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions, International Journal of Data Science and Analysis. Vol. 4, No. 2, 2018, pp. 32-37. doi: 10.11648/j.ijdsa.20180402.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Box, G. and K. Wilson, on the experimental attainment of optimum conditions, in Breakthroughs in statistics. 1992, Springer. p. 270-310.
[2]
Asadi, H., et al., Robust optimal motion cueing algorithm based on the linear quadratic regulator method and a genetic algorithm. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017. 47(2): p. 238-254.
[3]
Box, G. and N. Draper, A basis for the selection of a response surface design. Journal of the American Statistical Association, 1959. 54(287): p. 622-654.
[4]
Bose, R. and N. Draper, Second order rotatable designs in three dimensions. The Annals of Mathematical Statistics, 1959: p. 1097-1112.
[5]
Pukelsheim, F., Optimal design of experiments. Vol. 50. 1993: siam.
[6]
Box, G. and J. Hunter, Multi-factor experimental designs for exploring response surfaces. The Annals of Mathematical Statistics, 1957: p. 195-241.
[7]
Draper, N. R., Second order rotatable designs in four or more dimensions. The Annals of Mathematical Statistics, 1960. 31(1): p. 23-33.
[8]
Elfving, G., Optimum allocation in linear regression theory. The Annals of Mathematical Statistics, 1952. 23(2): p. 255-262.
[9]
Mwan, D., M. Kosgei, and S. Rambaei, DT-optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design.
[10]
Atkinson, A. C., DT-optimum designs for model discrimination and parameter estimation. Journal of Statistical planning and Inference, 2008. 138(1): p. 56-64.
[11]
Atkinson, A., A. Donev, and R. Tobias, Optimum experimental designs, with SAS, vol. 34 of Oxford Statistical Science Series. 2007, Oxford University Press Oxford, UK.
[12]
Mylona, K., Goos, P., & Jones, B. (2014). Optimal design of blocked and split-plot experiments for fixed effects and variance component estimation. Technometrics, 56(2), 132-144.
[13]
Youdim, K., Atkinson, A. C., Patan, M., Bogacka, B., & Johnson, P. (2010). Potential Application of D-Optimum Designs in the Efficient Investigation of Cytochrome P450 Inhibition Kinetic Models. Drug metabolism and disposition, dmd-11.
[14]
Nguyen, T. T., Bénech, H., Delaforge, M., & Lenuzza, N. (2016). Design optimisation for pharmacokinetic modeling of a cocktail of phenotyping drugs. Pharmaceutical statistics.
[15]
Kussmaul, R., Zogg, M., & Ermanni, P. (2018). An optimality criteria-based algorithm for efficient design optimization of laminated composites using concurrent resizing and scaling. Structural and Multidisciplinary Optimization, 1-16.
Browse journals by subject