Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)

Otieno-Roche Emily; Koske Joseph; Mutiso John

doi:doi:10.11648/j.ajtas.20170606.17

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Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)

Otieno-Roche Emily, Koske Joseph, Mutiso John

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)

Received: 2 June 2017 Accepted: 16 June 2017 Published: 7 December 2017

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Abstract

Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. A rotatable simplex design is one of the new designs that have been suggested for fitting second-order response surface models. In this article, we present a method for constructing weighted second order rotatable simplex designs (WRSD) which are more efficient than the ordinary rotatable simplex designs (RSD). Using moment matrices based on the Simplex and Factorial Designs, and the General Equivalence Theorem (GET) for D- and A- optimality, weighted rotatable simplex designs (WRSDs) were obtained. A- and D- optimality criterion was then used to establish the efficiency of the designs.

Published in	American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)
DOI	10.11648/j.ajtas.20170606.17
Page(s)	303-310
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), 2017. Published by Science Publishing Group

Keywords

D – Optimal, A – Optimal, Response Surface Designs, Second-Order Designs, Information Surface, Moment Matrices, Weighted Rotatable Simplex Designs

References

[1]	Box, G. E. P., & Draper, N. R. (1959). A basis for the selection of a response surface design. Journal of American Statistical Association, 54, 622-654.
[2]	Das, M. N., & Narasimham, V. L. (1962). Construction of rotatable designs through balanced incomplete block designs. Annals of Mathematical Statistics, 33(4), 1421-1439.
[3]	Das, R. N. (1997). Robust second order rotatable designs: Part I RSORD. Calcutta Statistical Association Bulletin, 47, 199-214.
[4]	Das, R. N. (1999). Robust Second Order Rotatable Designs: Part - II RSORD. Calcutta Statistical Association Bulletin, 49, 65-76.
[5]	Otieno-Roche E., Koske J. & Mutiso J. (2017). Construction of Second Order Rotatable Simplex Designs. Manuscript submitted for publication.
[6]	Panda, R. N., & Das, R. N. (1994). First order rotatable designs with correlated errors. Calcutta Statistical Association Bulletin, 44, 83-101.
[7]	Rajyalakshmi, K., & Victorbabu B. R. (2014). Construction of second order rotatable designs under tri-diagonal correlation structure of errors using central composite designs. Journal of Statistics: Advances in Theory and Applications, 11(2), 71-90.
[8]	Rajyalakshmi, K., & Victorbabu, B. R. (2011). Robust Second Order Rotatable Central Composite Designs. JP Journal of Fundamental and Applied Statistics, 1(2), 85-102.
[9]	Tyagi, B. N. (1964). Construction of second order and third order rotatable designs through pairwise balanced designs and doubly balanced designs. Calcutta Statistical Association Bulletin, 13, 150-162.
[10]	Victorbabu, B. R., & Rajyalakshmi, K. (2012). A new method of construction of robust second order rotatable designs using balanced incomplete block designs. Open Journal of Statistics, 2(2), 88-96.
[11]	Victorbabu, B. R., & Rajyalakshmi, K. (2012). Robust second order slope rotatable designs using balanced incomplete block designs. Open Journal of Statistics, 2(2), 65-77.

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APA Style

Otieno-Roche Emily, Koske Joseph, Mutiso John. (2017). Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd). American Journal of Theoretical and Applied Statistics, 6(6), 303-310. https://doi.org/10.11648/j.ajtas.20170606.17

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ACS Style

Otieno-Roche Emily; Koske Joseph; Mutiso John. Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd). Am. J. Theor. Appl. Stat. 2017, 6(6), 303-310. doi: 10.11648/j.ajtas.20170606.17

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AMA Style

Otieno-Roche Emily, Koske Joseph, Mutiso John. Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd). Am J Theor Appl Stat. 2017;6(6):303-310. doi: 10.11648/j.ajtas.20170606.17

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@article{10.11648/j.ajtas.20170606.17,
  author = {Otieno-Roche Emily and Koske Joseph and Mutiso John},
  title = {Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {6},
  pages = {303-310},
  doi = {10.11648/j.ajtas.20170606.17},
  url = {https://doi.org/10.11648/j.ajtas.20170606.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170606.17},
  abstract = {Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. A rotatable simplex design is one of the new designs that have been suggested for fitting second-order response surface models. In this article, we present a method for constructing weighted second order rotatable simplex designs (WRSD) which are more efficient than the ordinary rotatable simplex designs (RSD). Using moment matrices based on the Simplex and Factorial Designs, and the General Equivalence Theorem (GET) for D- and A- optimality, weighted rotatable simplex designs (WRSDs) were obtained. A- and D- optimality criterion was then used to establish the efficiency of the designs.},
 year = {2017}
}

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TY  - JOUR
T1  - Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)
AU  - Otieno-Roche Emily
AU  - Koske Joseph
AU  - Mutiso John
Y1  - 2017/12/07
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.17
DO  - 10.11648/j.ajtas.20170606.17
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 303
EP  - 310
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170606.17
AB  - Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. A rotatable simplex design is one of the new designs that have been suggested for fitting second-order response surface models. In this article, we present a method for constructing weighted second order rotatable simplex designs (WRSD) which are more efficient than the ordinary rotatable simplex designs (RSD). Using moment matrices based on the Simplex and Factorial Designs, and the General Equivalence Theorem (GET) for D- and A- optimality, weighted rotatable simplex designs (WRSDs) were obtained. A- and D- optimality criterion was then used to establish the efficiency of the designs.
VL  - 6
IS  - 6
ER  -

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Author Information

Otieno-Roche Emily

Department of Computer and Information Technology, Africa Nazarene University, Nairobi, Kenya
Koske Joseph

Department of Statistics and Computer Science, Moi University, Eldoret, Kenya
Mutiso John

Department of Statistics and Computer Science, Moi University, Eldoret, Kenya

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APA Style

Otieno-Roche Emily, Koske Joseph, Mutiso John. (2017). Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd). American Journal of Theoretical and Applied Statistics, 6(6), 303-310. https://doi.org/10.11648/j.ajtas.20170606.17

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ACS Style

Otieno-Roche Emily; Koske Joseph; Mutiso John. Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd). Am. J. Theor. Appl. Stat. 2017, 6(6), 303-310. doi: 10.11648/j.ajtas.20170606.17

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AMA Style

Otieno-Roche Emily, Koske Joseph, Mutiso John. Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd). Am J Theor Appl Stat. 2017;6(6):303-310. doi: 10.11648/j.ajtas.20170606.17

Copy | Download

@article{10.11648/j.ajtas.20170606.17,
  author = {Otieno-Roche Emily and Koske Joseph and Mutiso John},
  title = {Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {6},
  pages = {303-310},
  doi = {10.11648/j.ajtas.20170606.17},
  url = {https://doi.org/10.11648/j.ajtas.20170606.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170606.17},
  abstract = {Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. A rotatable simplex design is one of the new designs that have been suggested for fitting second-order response surface models. In this article, we present a method for constructing weighted second order rotatable simplex designs (WRSD) which are more efficient than the ordinary rotatable simplex designs (RSD). Using moment matrices based on the Simplex and Factorial Designs, and the General Equivalence Theorem (GET) for D- and A- optimality, weighted rotatable simplex designs (WRSDs) were obtained. A- and D- optimality criterion was then used to establish the efficiency of the designs.},
 year = {2017}
}

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TY  - JOUR
T1  - Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)
AU  - Otieno-Roche Emily
AU  - Koske Joseph
AU  - Mutiso John
Y1  - 2017/12/07
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.17
DO  - 10.11648/j.ajtas.20170606.17
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 303
EP  - 310
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170606.17
AB  - Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. A rotatable simplex design is one of the new designs that have been suggested for fitting second-order response surface models. In this article, we present a method for constructing weighted second order rotatable simplex designs (WRSD) which are more efficient than the ordinary rotatable simplex designs (RSD). Using moment matrices based on the Simplex and Factorial Designs, and the General Equivalence Theorem (GET) for D- and A- optimality, weighted rotatable simplex designs (WRSDs) were obtained. A- and D- optimality criterion was then used to establish the efficiency of the designs.
VL  - 6
IS  - 6
ER  -

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