Application of minimum projection uniformity criterion in complementary designs for q-level factorials

doi:10.1007/s11464-015-0446-2

Front. Math. China

2015, Vol. 10

Issue (2) : 339-350 https://doi.org/10.1007/s11464-015-0446-2

RESEARCH ARTICLE

Application of minimum projection uniformity criterion in complementary designs for q-level factorials

Hong QIN¹,Zhenghong WANG^1,^2,^*(

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1. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
2. School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China

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Abstract

We study the complementary design problem, which is to express the uniformity pattern of a q-level design in terms of that of its complementary design. Here, a pair of complementary designs form a design in which all the Hamming distances of any two distinct runs are the same, and the uniformity pattern proposed by H. Qin, Z. Wang, and K. Chatterjee [J. Statist. Plann. Inference, 2012, 142: 1170–1177] comes from discrete discrepancy for q-level designs. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity rule to assess and compare q-level factorials.

Keywords Discrete discrepancy uniformity pattern minimum projection uniformity (MPU) complementary design

Corresponding Author(s): Zhenghong WANG

Issue Date: 12 February 2015

Cite this article:

Hong QIN,Zhenghong WANG. Application of minimum projection uniformity criterion in complementary designs for q-level factorials[J]. Front. Math. China, 2015, 10(2): 339-350.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0446-2
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I2/339

1	Fang K, Qin H. Uniformity pattern and related criteria for two-level factorials. Sci China Ser A, 2005, 48: 1-11 https://doi.org/10.1360/03YS0155
2	Georgiou G, Koukouvinos C. Multi-level k-circulant supersaturated designs. Metrika, 2006, 64: 209-220 https://doi.org/10.1007/s00184-006-0045-z
3	He Y, Ai M. Complementary design theory for sliced equidistance designs. Statist Probab Lett, 2012, 82: 542-547 https://doi.org/10.1016/j.spl.2011.11.008
4	Hickernell F J, Liu M. Uniform designs limit aliasing. Biometrika, 2002, 89(4): 893-904 https://doi.org/10.1093/biomet/89.4.893
5	Lin D K J, Draper N R. Projection properties of Plackett and Burman designs. Technometrics, 1992, 34: 423-428
6	Liu M, Fang K, Hickernell F J. Connections among different criteria for asymmetrical fractional factorial designs. Statist Sinica, 2006, 16(4): 1285-1297
7	Liu Y, Liu M. Construction of supersaturated design with large number of factors by the complementary design method. Acta Math Appl Sin Engl Ser, 2013, 29: 253-262 https://doi.org/10.1007/s10255-013-0214-6
8	Mukerjee R, Wu C F J. On the existence of saturated and nearly saturated asymmetrical orthogonal arrays. Ann Statist, 1995, 23: 2102-2115 https://doi.org/10.1214/aos/1034713649
9	Qin H. Characterization of generalized aberration of some designs in terms of their complementary designs. J Statist Plann Inference, 2003, 117: 141-151 https://doi.org/10.1016/S0378-3758(02)00361-0
10	Qin H, Chatterjee K. Lower bounds for the uniformity pattern of asymmetric fractional factorials. Comm Statist Theory Methods, 2009, 38: 1383-1392 https://doi.org/10.1080/03610920802439161
11	Qin H, Fang K. Discrete discrepancy in factorial designs. Metrika, 2004, 60: 59-72 https://doi.org/10.1007/s001840300296
12	Qin H, Wang Z, Chatterjee K. Uniformity pattern and related criteria for q-level factorials. J Statist Plann Inference, 2012, 142: 1170-1177 https://doi.org/10.1016/j.jspi.2011.11.018
13	Song S, Qin H. Application of minimum projection uniformity criterion in complementary designs. Acta Math Sin (Engl Ser), 2010, 30B(1): 180-186
14	Suen C, Chen H, Wu C J F. Some identities on qn-m designs with application to minimum aberration designs. Ann Statist, 1997, 25: 1176-1188 https://doi.org/10.1214/aos/1069362743
15	Tang B, Wu C F J. Characterization of minimum aberration 2n-k designs in terms of their complementary designs. Ann Statist, 1996, 24: 2549-2559 https://doi.org/10.1214/aos/1032181168
16	Tang B, Deng L Y. Minimum G2-aberration for nonregular fractional designs. Ann Statist, 1999, 27: 1914-1926
17	Xu H, Wu C F J. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann Statist, 2001, 29: 549-560
18	Zhang S, Qin H. Minimum projection uniformity criterion and its application. Statist Probab Lett, 2006, 76: 634-640 https://doi.org/10.1016/j.spl.2005.09.019

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