Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions

Dennis Matundura Mwan; Mathew Kosgei

doi:doi:10.11648/j.ijdsa.20180402.11

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Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions

Dennis Matundura Mwan, Mathew Kosgei

Published in International Journal of Data Science and Analysis (Volume 4, Issue 2)

Received: 29 May 2018 Accepted: 6 July 2018 Published: 4 August 2018

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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.

Published in	International Journal of Data Science and Analysis (Volume 4, Issue 2)
DOI	10.11648/j.ijdsa.20180402.11
Page(s)	32-37
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Optimality Criteria, Compound Criteria, DT-optimum and CD-optimum

References

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[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.

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Dennis Matundura Mwan, Mathew Kosgei. (2018). 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, 4(2), 32-37. https://doi.org/10.11648/j.ijdsa.20180402.11

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ACS Style

Dennis Matundura Mwan; Mathew Kosgei. Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions. Int. J. Data Sci. Anal. 2018, 4(2), 32-37. doi: 10.11648/j.ijdsa.20180402.11

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AMA Style

Dennis Matundura Mwan, Mathew Kosgei. Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions. Int J Data Sci Anal. 2018;4(2):32-37. doi: 10.11648/j.ijdsa.20180402.11

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@article{10.11648/j.ijdsa.20180402.11,
  author = {Dennis Matundura Mwan and Mathew Kosgei},
  title = {Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions},
  journal = {International Journal of Data Science and Analysis},
  volume = {4},
  number = {2},
  pages = {32-37},
  doi = {10.11648/j.ijdsa.20180402.11},
  url = {https://doi.org/10.11648/j.ijdsa.20180402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20180402.11},
  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.},
 year = {2018}
}

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TY  - JOUR
T1  - Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions
AU  - Dennis Matundura Mwan
AU  - Mathew Kosgei
Y1  - 2018/08/04
PY  - 2018
N1  - https://doi.org/10.11648/j.ijdsa.20180402.11
DO  - 10.11648/j.ijdsa.20180402.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 32
EP  - 37
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20180402.11
AB  - 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.
VL  - 4
IS  - 2
ER  -

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Author Information

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

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APA Style

Dennis Matundura Mwan, Mathew Kosgei. (2018). 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, 4(2), 32-37. https://doi.org/10.11648/j.ijdsa.20180402.11

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ACS Style

Dennis Matundura Mwan; Mathew Kosgei. Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions. Int. J. Data Sci. Anal. 2018, 4(2), 32-37. doi: 10.11648/j.ijdsa.20180402.11

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AMA Style

Dennis Matundura Mwan, Mathew Kosgei. Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions. Int J Data Sci Anal. 2018;4(2):32-37. doi: 10.11648/j.ijdsa.20180402.11

Copy | Download

@article{10.11648/j.ijdsa.20180402.11,
  author = {Dennis Matundura Mwan and Mathew Kosgei},
  title = {Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions},
  journal = {International Journal of Data Science and Analysis},
  volume = {4},
  number = {2},
  pages = {32-37},
  doi = {10.11648/j.ijdsa.20180402.11},
  url = {https://doi.org/10.11648/j.ijdsa.20180402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20180402.11},
  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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Two Combined Alphabetic Optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design in Four Dimensions
AU  - Dennis Matundura Mwan
AU  - Mathew Kosgei
Y1  - 2018/08/04
PY  - 2018
N1  - https://doi.org/10.11648/j.ijdsa.20180402.11
DO  - 10.11648/j.ijdsa.20180402.11
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 32
EP  - 37
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20180402.11
AB  - 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.
VL  - 4
IS  - 2
ER  -

Copy | Download