CONFOUNDING STRUCTURE OF TWO-LEVEL NONREGULAR FACTORIAL DESIGNS

doi:10.1016/S0252-9602(12)60032-0

Abstract

Abstract:

In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregular design, a natural question is how to describe the confounding relations between its effects, is there any inner structure similar to regular designs? The aim of this article is to answer this basic question. Using coefficients of indicator function, confounding structure of nonregular fractional factorial designs is obtained as linear constrains on the values of effects. A method to estimate the sparse significant effects in an arbitrary nonregular design is given through an example.

Key words: Nonregular design, alias set, partial aliasing

CLC Number:

62K15

Ren Jun-Bai. CONFOUNDING STRUCTURE OF TWO-LEVEL NONREGULAR FACTORIAL DESIGNS[J].Acta mathematica scientia,Series B, 2012, 32(2): 488-498.

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References

[1] Mukerjee R, Wu C F J. A Modern Theory of Factorial Design. New York: Springer, 2006

[2] Hamada M, Wu C F J. Analysis of designed experiments with complex aliasing. J Quality Technology, 1992, 24: 130–137

[3] Deng L Y, Tang B. Generalized resolution and minimum aberration criteria for Plackett-Burman and other nonregular factorial designs. Statistica Sinica, 1999, 9: 1071–1082

[4] Tang B, Deng L Y. Minimum G2-aberration for nonregular fractional factorial designs. Annals of Statistics, 1999, 27: 1914–1926

[5] Xu H, Wu C F J. Generalized minimum aberration for asymmetrical fractional factorial designs. Annals of Statistics, 2001, 29: 1066–1077

[6] Xu H. Minimum moment aberration for nonregular fractional factorial designs and supersaturated designs. Statistica Sinica, 2003, 13: 691–708

[7] Fontana R, Pistone G, Rogantin M P. Classification of two-level factorial fractions. J Statist Plann Inference, 2000, 87: 149–172

[8] Ye K Q. Indicator function and its application in two-level factorial designs. Annals of Statistics, 2003, 31: 984–994

[9] Wu C F J, Hamada M. Experiments: Planning, Analysis, and Parameter Design Optimization. New York: Wiley, 2000

[10] Pistone G, Riccomagno E, Wynn H P. Algebraic statistics: Computational commutative algebra in statis-tics. Chapman&Hall, 2001

[11] Zhang R C, Li P, Zhao S L, Ai M Y. A general minimum lower-order confounding criterion for two-level regular designs. Statistica Sinica, 2008, 18(4): 1689–1705

[12] Yang Guijun, Liu Mingqian, Zhang Runchu. Weak minimum aberration and maximum number of clear two-factor interactions in 2m−p
IV designs. Science in China (Ser A Mathematics), 2005, 48(11): 1479–1487

[13] Sun D X, Wu C F J. Statistical Properties of Hadamard Matrices of Order 16//Kuo W. Quality Through Engineering Design. Elsevier Science Publishers, 1993: 169–179