A connection between uniformity and aberration in regular fractions of two-level factorials

Kai Tai Fang; Rahul Mukerjee

doi:10.1093/biomet/87.1.193

A connection between uniformity and aberration in regular fractions of two-level factorials

Kai Tai Fang
, Rahul Mukerjee

Research output: Contribution to journal › Journal article › peer-review

113 Citations (Scopus)

Abstract

We show a link between the two apparently unrelated areas of uniformity and minimum aberration. With reference to regular fractions of two-level factorials, we derive an expression for the centred L₂-discrepancy measure for uniformity in terms of the word-length pattern. This result indicates, in particular, excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration.

Original language	English
Pages (from-to)	193-198
Number of pages	6
Journal	Biometrika
Volume	87
Issue number	1
DOIs	https://doi.org/10.1093/biomet/87.1.193
Publication status	Published - 1 Mar 2000
Externally published	Yes

User-Defined Keywords

Centred L2-discrepancy
Fractional factorial design
Minimum aberration
Uniformity
Word-length pattern

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10.1093/biomet/87.1.193

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abstract = "We show a link between the two apparently unrelated areas of uniformity and minimum aberration. With reference to regular fractions of two-level factorials, we derive an expression for the centred L2-discrepancy measure for uniformity in terms of the word-length pattern. This result indicates, in particular, excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration.",

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AU - Fang, Kai Tai

AU - Mukerjee, Rahul

N1 - Funding information: This work was partially supported by the Hong Kong Baptist University, a grant from the Hong Kong University Grants Council and a grant form the Center for Management and Development Studies of the Indian Institute of Management in Calcutta. We thank the editor and a referee for very constructive suggestions. Publisher copyright: © 2000 Biometrika Trust

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N2 - We show a link between the two apparently unrelated areas of uniformity and minimum aberration. With reference to regular fractions of two-level factorials, we derive an expression for the centred L2-discrepancy measure for uniformity in terms of the word-length pattern. This result indicates, in particular, excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration.

AB - We show a link between the two apparently unrelated areas of uniformity and minimum aberration. With reference to regular fractions of two-level factorials, we derive an expression for the centred L2-discrepancy measure for uniformity in terms of the word-length pattern. This result indicates, in particular, excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration.

KW - Centred L2-discrepancy

KW - Fractional factorial design

KW - Minimum aberration

KW - Uniformity

KW - Word-length pattern

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DO - 10.1093/biomet/87.1.193

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SP - 193

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JO - Biometrika

JF - Biometrika

IS - 1

ER -

A connection between uniformity and aberration in regular fractions of two-level factorials

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