Optimal foldover plans for two-level nonregular orthogonal designs

William Li; Dennis K.J. Lin; Kenny Q. Ye

doi:10.1198/004017003000000177

Optimal foldover plans for two-level nonregular orthogonal designs

William Li, Dennis K.J. Lin, Kenny Q. Ye

Research output: Contribution to specialist publication › Article

64 Scopus citations

Abstract

This article considers optimal foldover plans for nonregular designs. By using the indicator function, we define words with fractional lengths. The extended word-length pattern is then used to select among non-regular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors is optimal for all-run and 20-run orthogonal designs. The optimal foldover plans for all 16-run (regular and nonregular) orthogonal designs are constructed and tabulated for practical use. Optimal foldover plans for higher-order orthogonal designs can be constructed in a similar manner.

Original language	English (US)
Pages	347-351
Number of pages	5
Volume	45
No	4
Specialist publication	Technometrics
DOIs	https://doi.org/10.1198/004017003000000177
State	Published - Nov 2003
Externally published	Yes

Keywords

Extended word length pattern
Foldover design
Generalized resolution
Indicator function
Orthogonal design

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1198/004017003000000177

Cite this

@misc{09e5a2345148469a8f358ff007a717b9,

title = "Optimal foldover plans for two-level nonregular orthogonal designs",

abstract = "This article considers optimal foldover plans for nonregular designs. By using the indicator function, we define words with fractional lengths. The extended word-length pattern is then used to select among non-regular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors is optimal for all-run and 20-run orthogonal designs. The optimal foldover plans for all 16-run (regular and nonregular) orthogonal designs are constructed and tabulated for practical use. Optimal foldover plans for higher-order orthogonal designs can be constructed in a similar manner.",

keywords = "Extended word length pattern, Foldover design, Generalized resolution, Indicator function, Orthogonal design",

author = "William Li and Lin, {Dennis K.J.} and Ye, {Kenny Q.}",

note = "Funding Information: This research was supported by the SupercomputingInstitute for Digital Simulation and Advanced Computation at the University of Minnesota. The authors thank the editor, an associate editor, and the two referees for their helpful comments and sug-gestionsin improvingan earlier version of the manuscript.They also thank Boxin Tang for reading an early draft of the manuscript and making helpful comments. Wilialm Li{\textquoteright}s research was also supported by a Research and Techaing Supplement from the Carlson School of Management, University of Minnesota. Dennis Lin is partially supported by National Security Agency grant MDA 904-02-1-0054.",

year = "2003",

month = nov,

doi = "10.1198/004017003000000177",

language = "English (US)",

volume = "45",

pages = "347--351",

journal = "Technometrics",

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publisher = "American Statistical Association",

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AU - Li, William

AU - Lin, Dennis K.J.

AU - Ye, Kenny Q.

N1 - Funding Information: This research was supported by the SupercomputingInstitute for Digital Simulation and Advanced Computation at the University of Minnesota. The authors thank the editor, an associate editor, and the two referees for their helpful comments and sug-gestionsin improvingan earlier version of the manuscript.They also thank Boxin Tang for reading an early draft of the manuscript and making helpful comments. Wilialm Li’s research was also supported by a Research and Techaing Supplement from the Carlson School of Management, University of Minnesota. Dennis Lin is partially supported by National Security Agency grant MDA 904-02-1-0054.

PY - 2003/11

Y1 - 2003/11

N2 - This article considers optimal foldover plans for nonregular designs. By using the indicator function, we define words with fractional lengths. The extended word-length pattern is then used to select among non-regular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors is optimal for all-run and 20-run orthogonal designs. The optimal foldover plans for all 16-run (regular and nonregular) orthogonal designs are constructed and tabulated for practical use. Optimal foldover plans for higher-order orthogonal designs can be constructed in a similar manner.

AB - This article considers optimal foldover plans for nonregular designs. By using the indicator function, we define words with fractional lengths. The extended word-length pattern is then used to select among non-regular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors is optimal for all-run and 20-run orthogonal designs. The optimal foldover plans for all 16-run (regular and nonregular) orthogonal designs are constructed and tabulated for practical use. Optimal foldover plans for higher-order orthogonal designs can be constructed in a similar manner.

KW - Extended word length pattern

KW - Foldover design

KW - Generalized resolution

KW - Indicator function

KW - Orthogonal design

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JO - Technometrics

JF - Technometrics

ER -

Optimal foldover plans for two-level nonregular orthogonal designs

Abstract

Keywords

ASJC Scopus subject areas

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