Skip to main content
SpringerLink
Log in

Classification of Three-word Indicator Functions of Two-level Factorial Designs

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Indicator functions have been in the literature for several years, and yet only a few of their properties have been examined. In this paper, we study some properties of indicator functions of two-level fractional factorial designs. For example, we show that there is no indicator function with only two words, and also classify all indicator functions with only three words. The results imply that there is no valuable non-regular design with only three or less words in its indicator function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Balakrishnan, N., Yang, P. (2006). Connections between the resolutions of general two-level factorial designs, The Annals of the Institute of Statistical Mathematics, (in press).

  • Cheng S.W., Ye K.Q. (2004). Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. The Annals of Statistics 32, 2168–2185

    Article  MATH  MathSciNet  Google Scholar 

  • Fontana R., Pistone G., Rogantin M.P. (2000). Classification of two-level factorial fractions. Journal of Statistical Planning and Inference 87, 149–172

    Article  MATH  MathSciNet  Google Scholar 

  • Li W., Lin D.K.J., Ye K.Q. (2003). Optimal foldover plans for non-regular orthogonal designs. Technometrics 45, 347–351

    Article  MathSciNet  Google Scholar 

  • Pistone G., Rogantin M.P. (2003). Indicator polynomial function for multilevel factorial designs, GROSTAT, VI.

  • Pistone G., Wynn H.P. (1996). Generalised confounding with Gröbner bases. Biometrika 83, 653–666

    Article  MATH  MathSciNet  Google Scholar 

  • Pistone G., Riccomagno E., Wynn H.P. (2001). Algebraic Statistics: Computational Commutative Algebra in Statistics. Chapman & Hall/CRC, London/West Palm Beach

    MATH  Google Scholar 

  • Ye K.Q. (2003). Indicator function and its application in two-level factorial designs. The Annals of Statistics 31, 984–994

    Article  MATH  MathSciNet  Google Scholar 

  • Ye K.Q. (2004). A note on regular fractional factorial designs. Statistica Sinica 14, 1069–1074

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    N. Balakrishnan

  2. Department of Mathematics and Statistics, University of Prince Edward Island, Charlottetown, PE, C1A 4P3, Canada

    Po Yang

Authors
  1. N. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Po Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Po Yang.

About this article

Cite this article

Balakrishnan, N., Yang, P. Classification of Three-word Indicator Functions of Two-level Factorial Designs. Ann Inst Stat Math 58, 595–608 (2006). https://doi.org/10.1007/s10463-006-0033-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10463-006-0033-0

Keywords

Search

Navigation