Uniformity in Fractional Factorials

Kai Tai Fang; Chang Xing Ma; Rahul Mukerjee

doi:10.1007/978-3-642-56046-0_15

Uniformity in Fractional Factorials

Kai Tai Fang, Chang Xing Ma, Rahul Mukerjee

Research output: Chapter in book/report/conference proceeding › Conference proceeding

Abstract

The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two- or three-level factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching for minimum aberration designs.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 2000
Subtitle of host publication	Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000
Editors	Kai Tai Fang, Harald Niederreiter, Fred J. Hickernell
Publisher	Springer Berlin Heidelberg
Pages	232–241
Number of pages	10
Edition	1st
ISBN (Electronic)	9783642560460
ISBN (Print)	9783540427186
DOIs	https://doi.org/10.1007/978-3-642-56046-0_15
Publication status	Published - 22 Jan 2002
Externally published	Yes
Event	4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000 - Hong Kong Baptist University, Hong Kong Duration: 27 Nov 2000 → 1 Dec 2000 https://www.math.hkbu.edu.hk/mcqmc/MCQMC2000.html (Link to conference website) https://link.springer.com/book/10.1007/978-3-642-56046-0 (Link to conference proceedings)

Conference

Conference	4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000
Country/Territory	Hong Kong
Period	27/11/00 → 1/12/00
Internet address	https://www.math.hkbu.edu.hk/mcqmc/MCQMC2000.html (Link to conference website) https://link.springer.com/book/10.1007/978-3-642-56046-0 (Link to conference proceedings)

User-Defined Keywords

Orthogonal Array
Prime Power
Fractional Factorial Design
Minimum Aberration
Projection Uniformity

Access to Document

10.1007/978-3-642-56046-0_15

Cite this

Fang, K. T., Ma, C. X., & Mukerjee, R. (2002). Uniformity in Fractional Factorials. In K. T. Fang, H. Niederreiter, & F. J. Hickernell (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000 (1st ed., pp. 232–241). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-56046-0_15

Fang, Kai Tai ; Ma, Chang Xing ; Mukerjee, Rahul. / Uniformity in Fractional Factorials. Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000. editor / Kai Tai Fang ; Harald Niederreiter ; Fred J. Hickernell. 1st. ed. Springer Berlin Heidelberg, 2002. pp. 232–241

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keywords = "Orthogonal Array, Prime Power, Fractional Factorial Design, Minimum Aberration, Projection Uniformity",

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note = "Funding information: We are thankful to Prof. Fred J. Hickernell and a referee for very constructive suggestions. This work was supported by grants from Hong KOng RGC, Statistics Reearch and Consultancy Centre, Hong Kong Baptist University and Centre for Management and Development Studies, Indian Institute of Management, Calcutta. Publisher copyright: {\textcopyright} 2002 Springer-Verlag Berlin Heidelberg; 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000 ; Conference date: 27-11-2000 Through 01-12-2000",

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Fang, KT, Ma, CX & Mukerjee, R 2002, Uniformity in Fractional Factorials. in KT Fang, H Niederreiter & FJ Hickernell (eds), Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000. 1st edn, Springer Berlin Heidelberg, pp. 232–241, 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2000, Hong Kong, 27/11/00. https://doi.org/10.1007/978-3-642-56046-0_15

Uniformity in Fractional Factorials. / Fang, Kai Tai; Ma, Chang Xing; Mukerjee, Rahul.
Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000. ed. / Kai Tai Fang; Harald Niederreiter; Fred J. Hickernell. 1st. ed. Springer Berlin Heidelberg, 2002. p. 232–241.

Research output: Chapter in book/report/conference proceeding › Conference proceeding

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N1 - Funding information: We are thankful to Prof. Fred J. Hickernell and a referee for very constructive suggestions. This work was supported by grants from Hong KOng RGC, Statistics Reearch and Consultancy Centre, Hong Kong Baptist University and Centre for Management and Development Studies, Indian Institute of Management, Calcutta. Publisher copyright: © 2002 Springer-Verlag Berlin Heidelberg

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Y1 - 2002/1/22

N2 - The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two- or three-level factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching for minimum aberration designs.

AB - The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two- or three-level factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching for minimum aberration designs.

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Fang KT, Ma CX, Mukerjee R. Uniformity in Fractional Factorials. In Fang KT, Niederreiter H, Hickernell FJ, editors, Monte Carlo and Quasi-Monte Carlo Methods 2000: Proceedings of a Conference held at Hong Kong Baptist University, Hong Kong SAR, China, November 27 – December 1, 2000. 1st ed. Springer Berlin Heidelberg. 2002. p. 232–241 doi: 10.1007/978-3-642-56046-0_15

Uniformity in Fractional Factorials

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