Complete enumeration of two-level orthogonal arrays of strength d with d + 2 constraints

John Stufken, Boxin Tang

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d + 2 constraints for any d and any run size n = λ2d. Our results not only give the number of nonisomorphic orthogonal arrays for given d and n, but also provide a systematic way of explicitly constructing these arrays. Our approach to the problem is to make use of the recently developed theory of J -characteristics for fractional factorial designs. Besides the general theoretical results, the paper presents some results from applications of the theory to orthogonal arrays of strength two, three and four.

Original languageEnglish (US)
Pages (from-to)793-814
Number of pages22
JournalAnnals of Statistics
Volume35
Issue number2
DOIs
StatePublished - Apr 2007
Externally publishedYes

Fingerprint

Orthogonal Array
Enumeration
Fractional Factorial Design
Orthogonal array

Keywords

  • Design resolution
  • Fractional factorial design
  • Hadamard matrix
  • Hadamard transform
  • Indicator function
  • Isomorphism
  • J-characteristic
  • Minimum aberration

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Complete enumeration of two-level orthogonal arrays of strength d with d + 2 constraints. / Stufken, John; Tang, Boxin.

In: Annals of Statistics, Vol. 35, No. 2, 04.2007, p. 793-814.

Research output: Contribution to journalArticle

Stufken, John ; Tang, Boxin. / Complete enumeration of two-level orthogonal arrays of strength d with d + 2 constraints. In: Annals of Statistics. 2007 ; Vol. 35, No. 2. pp. 793-814.
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