Indicator function and its application in two-level factorial designs

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83 Scopus citations


A two-level factorial design can be uniquely represented by a polynomial indicator function. Therefore, properties of factorial designs can be studied through their indicator functions. This paper shows that the indicator function is an effective tool in studying two-level factorial designs. The indicator function is used to generalize the aberration criterion of a regular two-level fractional factorial design to all two-level factorial designs. An important identity of generalized aberration is proved. The connection between a uniformity measure and aberration is also extended to all two-level factorial designs.

Original languageEnglish (US)
Pages (from-to)984-994
Number of pages11
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 2003
Externally publishedYes


  • Generalized aberration
  • Orthogonality
  • Projection properties
  • Uniform design

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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