On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD
American Journal of Theoretical and Applied Statistics
Volume 9, Issue 6, November 2020, Pages: 263-266
Received: Sep. 28, 2020; Accepted: Oct. 19, 2020; Published: Oct. 30, 2020
Views 41      Downloads 9
Authors
Puja Thapliyal, Department of Statistics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
Veena Budhraja, Department of Statistics, Sri Venkateswara College, South Campus, University of Delhi, Delhi, India
Article Tools
Follow on us
Abstract
Randomization is one of the powerful tools to analyze, construct and draw valid and unbiased conclusions about the factorial design. But in some experimental situations, the technique may not perform equally well to draw valid inferences. These situations may arise due to an influence of external variations like the ageing of catalyst, known as Time-trend or Trend, on the response. Thus, instead of randomizing the run order of the factorial design, systematically arranging the order of treatments that is free of variations, neutralizes the adverse effect of Trend. Such systematic designs are known as Trend Free designs. The design gives not only higher importance to the treatments but also ensures the independence of treatments for further analysis. Methods for constructing trend-free run order of two-level designs have been studied and developed by many authors. The proposed run order for 2k and 2k-p design that are linear and quadratic trend free. Systematic run order has been constructed not only to eliminate the effect of the linear and quadratic trend but also to improve design performance in the presence of a trend. This article provides another technique to develop trend free run order of two-level factorial design using Symmetric Balanced Incomplete Block Design.
Keywords
Trend Free Designs, Factorial Designs, Generalized Foldover Scheme, BIBD
To cite this article
Puja Thapliyal, Veena Budhraja, On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD, American Journal of Theoretical and Applied Statistics. Vol. 9, No. 6, 2020, pp. 263-266. doi: 10.11648/j.ajtas.20200906.11
Copyright
Copyright © 2020 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.
References
[1]
D. R. Cox, “Some Systematic Experimental Designs,” Biometrika, Vol. 38, 1951, pp. 312-323.
[2]
G. E. P. Box, “Multi-factor Designs of First Order,” Biometrika, Vol. 39, 1952, pp. 49-57.
[3]
M. Jacroux, “On the Construction of Trend Resistant Mixed Level Factorial Run Orders,” Annals of Statistics, Vol. 22, 1994, pp. 904-916.
[4]
G. E. P. Box, and W. A. Hay, “Statistical design for the Efficient Removal of Trend so occurring in a Comparative Experiment with an Application in Biological Assay,” Biometrics, Vol. 9, 1953, pp. 304-319.
[5]
H. H. Hill, “Experimental Designs to adjust for time trends,” Technometrics, Vol. 2, 1960. pp. 67-82.
[6]
C. Daniel, and F. Wilcoxon, “Factorial 2p-q plans robust against Linear and Quadratic Trends,” Technometrics. Vol. 8, 1966, pp. 259-278.
[7]
D. C. Coster, and C. S. Cheng, “Minimum Cost Trend Free Run Orders of Fractional Factorial Design,” The Annals of Statistics, Vol. 16 (3), 1988, pp. 1188-1205.
[8]
C. S. Cheng, “Run Orders of Factorial Designs,” Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Lucein. Vol. 2, 1985, pp. 619-633.
[9]
C. S. Cheng, “Construction of Run Orders of Factorial Design,” Statistical Design and Analysis of Industrial Experiment, Marcel Dekkar, New York. 1990, pp. 423-439.
[10]
C. S. Cheng, and M. Jacroux, “On the Construction of Trend Free Run Order of Two-Level Factorial Designs,” American Statistical Association, Vol. 83, 1988, pp. 1152-1157.
[11]
P. Singh, P. Thapliyal, and V. Budhraja, “Construction of Fractional Factorial Designs with some Linear Trend Free Effects through Finite Field,” Journal of combinatorics, Information and System Sciences, Vol. 39 (1-2), 2014, pp. 57-76.
[12]
P. Singh, P. Thapliyal, and V. Budhraja, “Construction of Linear Trend-free fractional factorial designs using linear codes,” International journal of agricultural and statistical sciences, Vol. 12 (1), 2016, pp. 13-19.
[13]
R. W. Mee, and A. V. Ramanova,). “Constructing and Analyzing two-level\trend robust designs,” Quality Engineering, Vol. 22 (4), 2010, pp. 306-316.
[14]
H. Hilow, “Minimum cost linear trend free fractional factorial designs,” Journal of statistical theory and practice Vol. 6, 2012, pp. 580-589.
[15]
A. S. Hedayat, N. J. A, Sloane, and J. Stufken. Orthogonal arrays; Theory and Applications, Springer-Verlag, New York. 1999.
[16]
C. R. Rao, “Some Combinatorial Problems of Arrays and Applications to Design of Experiments,” A Survey of Combinatorial Theory, in N. Srivastava ed., Amsterdam, North-Holland. 1973, pp. 349-359.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186