# Indicator function and its application in two-level factorial designs

Research output: Contribution to journalArticle

64 Citations (Scopus)

### Abstract

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 language English (US) 984-994 11 Annals of Statistics 31 3 https://doi.org/10.1214/aos/1056562470 Published - Jun 2003 Yes

### Fingerprint

Indicator function
Factorial Design
Aberration
Fractional Factorial Design
Polynomial function
Uniformity
Factorial design
Generalise

### Keywords

• Generalized aberration
• Orthogonality
• Projection properties
• Uniform design

### ASJC Scopus subject areas

• Mathematics(all)
• Statistics and Probability

### Cite this

In: Annals of Statistics, Vol. 31, No. 3, 06.2003, p. 984-994.

Research output: Contribution to journalArticle

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abstract = "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.",
keywords = "Generalized aberration, Orthogonality, Projection properties, Uniform design",
author = "Ye, {Qian K.}",
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language = "English (US)",
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AB - 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.

KW - Generalized aberration

KW - Orthogonality

KW - Projection properties

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