Recent developments in nonregular fractional factorial designs
Hongquan Xu, Frederick K.H. Phoa, and Weng Kee Wong
Source: Statist. Surv. Volume 3
(2009), 18-46.
Abstract
Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditional analysis focuses on main effects only. Hamada and Wu (1992) went beyond the traditional approach and proposed an analysis strategy to demonstrate that some interactions could be entertained and estimated beyond a few significant main effects. Their groundbreaking work stimulated much of the recent developments in optimality criteria, construction and analysis of nonregular designs. This paper reviews important developments in nonregular designs, including projection properties, generalized resolution, generalized minimum aberration criteria, optimality results, construction methods and analysis strategies.
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Keywords: Factor screening; generalized minimum aberration; generalized resolution; minimum moment aberration; orthogonal array; Plackett-Burman design; projectivity
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Permanent link to this document: http://projecteuclid.org/euclid.ssu/1244555797
Digital Object Identifier: doi:10.1214/08-SS040
Mathematical Reviews number (MathSciNet): MR2520978
Zentralblatt MATH identifier: 05719271
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Project Euclid: euclid.aos/1032181168
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Mathematical Reviews (MathSciNet): MR1782491
Zentralblatt MATH: 0963.62074
Digital Object Identifier: doi:10.1093/biomet/87.2.467
JSTOR: links.jstor.org
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Zentralblatt MATH: 1060.62088
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Mathematical Reviews (MathSciNet): MR1329295
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Mathematical Reviews (MathSciNet): MR1248029
Zentralblatt MATH: 0800.62483
Digital Object Identifier: doi:10.1093/biomet/80.3.661
JSTOR: links.jstor.org
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Mathematical Reviews (MathSciNet): MR1780411
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Mathematical Reviews (MathSciNet): MR1939683
Digital Object Identifier: doi:10.1198/004017002188618554
JSTOR: links.jstor.org
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Mathematical Reviews (MathSciNet): MR1997169
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Mathematical Reviews (MathSciNet): MR2201366
Zentralblatt MATH: 1094.62095
Digital Object Identifier: doi:10.1093/biomet/92.2.385
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Mathematical Reviews (MathSciNet): MR2274993
Digital Object Identifier: doi:10.1007/s00184-005-0408-x
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Mathematical Reviews (MathSciNet): MR2291509
Zentralblatt MATH: 1106.62087
Digital Object Identifier: doi:10.1214/009053606000000777
Project Euclid: euclid.aos/1169571806
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Mathematical Reviews (MathSciNet): MR2562273
Digital Object Identifier: doi:10.1198/tech.2009.07120
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Mathematical Reviews (MathSciNet): MR2387979
Zentralblatt MATH: 1132.62059
Digital Object Identifier: doi:10.1214/009005360700000712
Project Euclid: euclid.aos/1201877309
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Mathematical Reviews (MathSciNet): MR2188074
Digital Object Identifier: doi:10.1198/004017004000000617
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Mathematical Reviews (MathSciNet): MR2299181
Zentralblatt MATH: 1104.62090
Digital Object Identifier: doi:10.1016/j.jspi.2005.05.002
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Mathematical Reviews (MathSciNet): MR2397390
Zentralblatt MATH: 1133.62056
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Mathematical Reviews (MathSciNet): MR1869240
Digital Object Identifier: doi:10.1214/aos/1013699993
Project Euclid: euclid.aos/1013699993
Xu, H. and Wu, C.F.J. (2005). Construction of optimal multi-level supersaturated designs., Ann. Statist., 33, 2811–2836.
Mathematical Reviews (MathSciNet): MR2253103
Zentralblatt MATH: 1084.62070
Digital Object Identifier: doi:10.1214/009053605000000688
Project Euclid: euclid.aos/1140191674
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Mathematical Reviews (MathSciNet): MR2082498
Digital Object Identifier: doi:10.1198/004017004000000310
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Mathematical Reviews (MathSciNet): MR2344643
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Mathematical Reviews (MathSciNet): MR1994738
Zentralblatt MATH: 1028.62061
Digital Object Identifier: doi:10.1214/aos/1056562470
Project Euclid: euclid.aos/1056562470
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Mathematical Reviews (MathSciNet): MR2126340
Zentralblatt MATH: 1060.62089
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Mathematical Reviews (MathSciNet): MR2414515
Digital Object Identifier: doi:10.1198/004017007000000173
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Mathematical Reviews (MathSciNet): MR2253104
Zentralblatt MATH: 1084.62071
Digital Object Identifier: doi:10.1214/009053605000000679
Project Euclid: euclid.aos/1140191675
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