Construction of Second Order Rotatable Simplex Designs

Otieno-Roche Emily; Koske Joseph; Mutiso John

doi:doi:10.11648/j.ajtas.20170606.16

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Construction of Second Order Rotatable Simplex Designs

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

Rotatable designs are mainly for the exploration of response surfaces. These designs provide the preferred property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction. Initially, they were constructed through geometrical configurations and several second order designs were obtained. Full Factorial Design of Experiment provides the most response information about factor main effects and interactions, the process model’s coefficients for all factors and interactions, and when validated, allows process to be optimized. On the other hand, mixture designs are a special case of response surface designs where prediction and optimization are the main goals. These designs usually predict all possible formulations of the ingredients however, little or no research has been done incorporating rotatability with the mixture designs. This paper therefore aims at constructing Rotatable Simplex Designs (RSDs) using the properties of Simplex - Lattice Designs (SLDs) in connection with Full Factorial Designs (FFDs).

Published in	American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)
DOI	10.11648/j.ajtas.20170606.16
Page(s)	297-302
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

Response Surface Designs, Second-Order Rotatable Designs (SORD), Mixture Designs, Moment Matrices, Central Composite 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]	Myers, R., Khuri, A., & Carter, W. (1989). Response Surface Methodology: 1966-1988. Technometrics, 31(2), 137-157. doi: 10.2307/1268813.
[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 Second Order Rotatable Simplex Designs. American Journal of Theoretical and Applied Statistics, 6(6), 297-302. https://doi.org/10.11648/j.ajtas.20170606.16

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ACS Style

Otieno-Roche Emily; Koske Joseph; Mutiso John. Construction of Second Order Rotatable Simplex Designs. Am. J. Theor. Appl. Stat. 2017, 6(6), 297-302. doi: 10.11648/j.ajtas.20170606.16

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AMA Style

Otieno-Roche Emily, Koske Joseph, Mutiso John. Construction of Second Order Rotatable Simplex Designs. Am J Theor Appl Stat. 2017;6(6):297-302. doi: 10.11648/j.ajtas.20170606.16

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@article{10.11648/j.ajtas.20170606.16,
  author = {Otieno-Roche Emily and Koske Joseph and Mutiso John},
  title = {Construction of Second Order Rotatable Simplex Designs},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {6},
  pages = {297-302},
  doi = {10.11648/j.ajtas.20170606.16},
  url = {https://doi.org/10.11648/j.ajtas.20170606.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170606.16},
  abstract = {Rotatable designs are mainly for the exploration of response surfaces. These designs provide the preferred property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction. Initially, they were constructed through geometrical configurations and several second order designs were obtained. Full Factorial Design of Experiment provides the most response information about factor main effects and interactions, the process model’s coefficients for all factors and interactions, and when validated, allows process to be optimized. On the other hand, mixture designs are a special case of response surface designs where prediction and optimization are the main goals. These designs usually predict all possible formulations of the ingredients however, little or no research has been done incorporating rotatability with the mixture designs. This paper therefore aims at constructing Rotatable Simplex Designs (RSDs) using the properties of Simplex - Lattice Designs (SLDs) in connection with Full Factorial Designs (FFDs).},
 year = {2017}
}

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TY  - JOUR
T1  - Construction of Second Order Rotatable Simplex Designs
AU  - Otieno-Roche Emily
AU  - Koske Joseph
AU  - Mutiso John
Y1  - 2017/12/07
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.16
DO  - 10.11648/j.ajtas.20170606.16
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  - 297
EP  - 302
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170606.16
AB  - Rotatable designs are mainly for the exploration of response surfaces. These designs provide the preferred property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction. Initially, they were constructed through geometrical configurations and several second order designs were obtained. Full Factorial Design of Experiment provides the most response information about factor main effects and interactions, the process model’s coefficients for all factors and interactions, and when validated, allows process to be optimized. On the other hand, mixture designs are a special case of response surface designs where prediction and optimization are the main goals. These designs usually predict all possible formulations of the ingredients however, little or no research has been done incorporating rotatability with the mixture designs. This paper therefore aims at constructing Rotatable Simplex Designs (RSDs) using the properties of Simplex - Lattice Designs (SLDs) in connection with Full Factorial Designs (FFDs).
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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Plain Text BibTeX RIS

APA Style

Otieno-Roche Emily, Koske Joseph, Mutiso John. (2017). Construction of Second Order Rotatable Simplex Designs. American Journal of Theoretical and Applied Statistics, 6(6), 297-302. https://doi.org/10.11648/j.ajtas.20170606.16

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ACS Style

Otieno-Roche Emily; Koske Joseph; Mutiso John. Construction of Second Order Rotatable Simplex Designs. Am. J. Theor. Appl. Stat. 2017, 6(6), 297-302. doi: 10.11648/j.ajtas.20170606.16

Copy | Download

AMA Style

Otieno-Roche Emily, Koske Joseph, Mutiso John. Construction of Second Order Rotatable Simplex Designs. Am J Theor Appl Stat. 2017;6(6):297-302. doi: 10.11648/j.ajtas.20170606.16

Copy | Download

@article{10.11648/j.ajtas.20170606.16,
  author = {Otieno-Roche Emily and Koske Joseph and Mutiso John},
  title = {Construction of Second Order Rotatable Simplex Designs},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {6},
  pages = {297-302},
  doi = {10.11648/j.ajtas.20170606.16},
  url = {https://doi.org/10.11648/j.ajtas.20170606.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170606.16},
  abstract = {Rotatable designs are mainly for the exploration of response surfaces. These designs provide the preferred property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction. Initially, they were constructed through geometrical configurations and several second order designs were obtained. Full Factorial Design of Experiment provides the most response information about factor main effects and interactions, the process model’s coefficients for all factors and interactions, and when validated, allows process to be optimized. On the other hand, mixture designs are a special case of response surface designs where prediction and optimization are the main goals. These designs usually predict all possible formulations of the ingredients however, little or no research has been done incorporating rotatability with the mixture designs. This paper therefore aims at constructing Rotatable Simplex Designs (RSDs) using the properties of Simplex - Lattice Designs (SLDs) in connection with Full Factorial Designs (FFDs).},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Construction of Second Order Rotatable Simplex Designs
AU  - Otieno-Roche Emily
AU  - Koske Joseph
AU  - Mutiso John
Y1  - 2017/12/07
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.16
DO  - 10.11648/j.ajtas.20170606.16
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  - 297
EP  - 302
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170606.16
AB  - Rotatable designs are mainly for the exploration of response surfaces. These designs provide the preferred property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction. Initially, they were constructed through geometrical configurations and several second order designs were obtained. Full Factorial Design of Experiment provides the most response information about factor main effects and interactions, the process model’s coefficients for all factors and interactions, and when validated, allows process to be optimized. On the other hand, mixture designs are a special case of response surface designs where prediction and optimization are the main goals. These designs usually predict all possible formulations of the ingredients however, little or no research has been done incorporating rotatability with the mixture designs. This paper therefore aims at constructing Rotatable Simplex Designs (RSDs) using the properties of Simplex - Lattice Designs (SLDs) in connection with Full Factorial Designs (FFDs).
VL  - 6
IS  - 6
ER  -

Copy | Download