On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD

Puja Thapliyal; Veena Budhraja

doi:doi:10.11648/j.ajtas.20200906.11

| Peer-Reviewed

On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD

Puja Thapliyal, Veena Budhraja

Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 6)

Received: 28 September 2020 Accepted: 19 October 2020 Published: 30 October 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 9, Issue 6)
DOI	10.11648/j.ajtas.20200906.11
Page(s)	263-266
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), 2024. Published by Science Publishing Group

Keywords

Trend Free Designs, Factorial Designs, Generalized Foldover Scheme, BIBD

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.

Cite This Article

Plain Text BibTeX RIS

APA Style

Puja Thapliyal, Veena Budhraja. (2020). On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD. American Journal of Theoretical and Applied Statistics, 9(6), 263-266. https://doi.org/10.11648/j.ajtas.20200906.11

Copy | Download

ACS Style

Puja Thapliyal; Veena Budhraja. On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD. Am. J. Theor. Appl. Stat. 2020, 9(6), 263-266. doi: 10.11648/j.ajtas.20200906.11

Copy | Download

AMA Style

Puja Thapliyal, Veena Budhraja. On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD. Am J Theor Appl Stat. 2020;9(6):263-266. doi: 10.11648/j.ajtas.20200906.11

Copy | Download

@article{10.11648/j.ajtas.20200906.11,
  author = {Puja Thapliyal and Veena Budhraja},
  title = {On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {6},
  pages = {263-266},
  doi = {10.11648/j.ajtas.20200906.11},
  url = {https://doi.org/10.11648/j.ajtas.20200906.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200906.11},
  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.},
 year = {2020}
}

Copy | Download

TY - JOUR
T1 - On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD
AU - Puja Thapliyal
AU - Veena Budhraja
Y1 - 2020/10/30
PY - 2020
N1 - https://doi.org/10.11648/j.ajtas.20200906.11
DO - 10.11648/j.ajtas.20200906.11
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 - 263
EP - 266
PB - Science Publishing Group
SN - 2326-9006
UR - https://doi.org/10.11648/j.ajtas.20200906.11
AB - 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.
VL - 9
IS - 6
ER -

Copy | Download

Author Information

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Puja Thapliyal, Veena Budhraja. (2020). On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD. American Journal of Theoretical and Applied Statistics, 9(6), 263-266. https://doi.org/10.11648/j.ajtas.20200906.11

Copy | Download

ACS Style

Puja Thapliyal; Veena Budhraja. On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD. Am. J. Theor. Appl. Stat. 2020, 9(6), 263-266. doi: 10.11648/j.ajtas.20200906.11

Copy | Download

AMA Style

Puja Thapliyal, Veena Budhraja. On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD. Am J Theor Appl Stat. 2020;9(6):263-266. doi: 10.11648/j.ajtas.20200906.11

Copy | Download

@article{10.11648/j.ajtas.20200906.11,
  author = {Puja Thapliyal and Veena Budhraja},
  title = {On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {6},
  pages = {263-266},
  doi = {10.11648/j.ajtas.20200906.11},
  url = {https://doi.org/10.11648/j.ajtas.20200906.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200906.11},
  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.},
 year = {2020}
}

Copy | Download