Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 6, November 2017, Pages: 303-310
Received: Jun. 2, 2017;
Accepted: Jun. 16, 2017;
Published: Dec. 7, 2017
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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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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.
D – Optimal, A – Optimal, Response Surface Designs, Second-Order Designs, Information Surface, Moment Matrices, Weighted Rotatable Simplex Designs
To cite this article
Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd), American Journal of Theoretical and Applied Statistics.
Vol. 6, No. 6,
2017, pp. 303-310.
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.
Otieno-Roche E., Koske J. & Mutiso J. (2017). Construction of Second Order Rotatable Simplex Designs. Manuscript submitted for publication.
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.