Construction of Second Order Rotatable Simplex Designs
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 6, November 2017, Pages: 297-302
Received: Jun. 2, 2017;
Accepted: Jun. 16, 2017;
Published: Dec. 7, 2017
Views 207 Downloads 14
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
Follow on us
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).
Response Surface Designs, Second-Order Rotatable Designs (SORD), Mixture Designs, Moment Matrices, Central Composite Designs
To cite this article
Construction of Second Order Rotatable Simplex Designs, American Journal of Theoretical and Applied Statistics.
Vol. 6, No. 6,
2017, pp. 297-302.
Copyright © 2017 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.
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.
Das, M. N., & Narasimham, V. L. (1962). Construction of rotatable designs through balanced incomplete block designs. Annals of Mathematical Statistics, 33(4), 1421-1439.
Das, R. N. (1997). Robust second order rotatable designs: Part I RSORD. Calcutta Statistical Association Bulletin, 47, 199-214.
Das, R. N. (1999). Robust Second Order Rotatable Designs: Part - II RSORD. Calcutta Statistical Association Bulletin, 49, 65-76.
Myers, R., Khuri, A., & Carter, W. (1989). Response Surface Methodology: 1966-1988. Technometrics, 31(2), 137-157. doi: 10.2307/1268813.
Panda, R. N., & Das, R. N. (1994). First order rotatable designs with correlated errors. Calcutta Statistical Association Bulletin, 44, 83-101.
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.
Rajyalakshmi, K., & Victorbabu, B. R. (2011). Robust Second Order Rotatable Central Composite Designs. JP Journal of Fundamental and Applied Statistics, 1(2), 85-102.
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.
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.
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.