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Journal of Statistical Theory and Practice

, Volume 9, Issue 2, pp 436–462 | Cite as

On the Joint Use of the Foldover and Partial Confounding for the Construction of Follow-Up Two-Level Blocked Fractional Factorial Designs

  • Mike Jacroux
  • Bonni Kealy-Dichone
Article

Abstract

In this article, we consider experimental situations where a regular fractional factorial design is initially used to study m two-level factors using n = 2mk experimental units arranged in 2p blocks of size 2mkp but where a follow-up design is desired to further study main effects and two-factor interactions. A typical follow-up would consist of folding over some of the experimental factors but using the same blocking scheme for the foldover design. Here, we consider the joint use of the foldover and the use of a different blocking scheme in the follow-up design to generate alternative combined designs that outperform the combined designs obtained using previously given procedures in terms of estimability of two-factor interactions, estimation capacity, or both.

Keywords

Design matrix Estimable effect Estimation capacity 

AMS Subject Classification: Primary

62K15 

AMS Subject Classification: Secondary

62K05 

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References

  1. Ai, M. Y., X. Xu, and C.F. Wu. 2010. Optimal blocking and foldover plans for regular two-level designs. Stat. Sinica, 20, 183–207.MathSciNetzbMATHGoogle Scholar
  2. Box, G. E. P., and J. S. Hunter. 1961. The 2k−p fractional factorial designs. Technometrics, 3, 311–351, 449–458.MathSciNetGoogle Scholar
  3. Chen, J., and C. F. J. Wu. 1991. Some results on Sn−f fractional factorial designs with minimum aberrations or optimal moments. Ann. Stat., 19, 1028–1041.CrossRefGoogle Scholar
  4. Chen, J., D. X. Sun, and C. F. J. Wu. 1993. A catalogue of two-level and three-level fractional factorial designs with small runs. Int. Stat. Rev., 61, 131–145.CrossRefGoogle Scholar
  5. Franklin, M. F. 1984. Constructing tables of minimum aberration 2k−p designs. Technometrics, 26, 225–232.MathSciNetGoogle Scholar
  6. Fries, A., and W. G. Hunter. 1980. Minimum aberration 2k−p designs. Technometrics, 22, 601–608.MathSciNetzbMATHGoogle Scholar
  7. Li, F., and M. Jacroux. 2007. Optimal foldover plans for blocked 2m−k fractional factorial designs. J. Stat. Plan. Inference, 137, 2434–2452.zbMATHGoogle Scholar
  8. Li, W., and D. K. J. Lin. 2003. Optimal foldover plans for fractional factorial designs. Technometrics, 45, 142–149.MathSciNetCrossRefGoogle Scholar
  9. Sun, D. X., C. F. J. Wu, and Y. Chen. 1997. Optimal blocking schemes for 2n and 2n−k designs. Technometrics, 39, 298–301.MathSciNetGoogle Scholar

Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.Department of StatisticsWashington State UniversityPullmanUSA
  2. 2.Department of MathematicsGonzaga UniversitySpokaneUSA

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