Frontiers of Mathematics in China >
Application of minimum projection uniformity criterion in complementary designs for q-level factorials
Received date: 02 Aug 2013
Accepted date: 11 Dec 2014
Published date: 12 Feb 2015
Copyright
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.
Hong QIN , Zhenghong WANG . Application of minimum projection uniformity criterion in complementary designs for q-level factorials[J]. Frontiers of Mathematics in China, 2015 , 10(2) : 339 -350 . DOI: 10.1007/s11464-015-0446-2
| 1 |
Fang K, Qin H. Uniformity pattern and related criteria for two-level factorials. Sci China Ser A, 2005, 48: 1-11
|
| 2 |
Georgiou G, Koukouvinos C. Multi-level k-circulant supersaturated designs. Metrika, 2006, 64: 209-220
|
| 3 |
He Y, Ai M. Complementary design theory for sliced equidistance designs. Statist Probab Lett, 2012, 82: 542-547
|
| 4 |
Hickernell F J, Liu M. Uniform designs limit aliasing. Biometrika, 2002, 89(4): 893-904
|
| 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
|
| 8 |
Mukerjee R, Wu C F J. On the existence of saturated and nearly saturated asymmetrical orthogonal arrays. Ann Statist, 1995, 23: 2102-2115
|
| 9 |
Qin H. Characterization of generalized aberration of some designs in terms of their complementary designs. J Statist Plann Inference, 2003, 117: 141-151
|
| 10 |
Qin H, Chatterjee K. Lower bounds for the uniformity pattern of asymmetric fractional factorials. Comm Statist Theory Methods, 2009, 38: 1383-1392
|
| 11 |
Qin H, Fang K. Discrete discrepancy in factorial designs. Metrika, 2004, 60: 59-72
|
| 12 |
Qin H, Wang Z, Chatterjee K. Uniformity pattern and related criteria for q-level factorials. J Statist Plann Inference, 2012, 142: 1170-1177
|
| 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
|
| 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
|
| 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
|
/
| 〈 |
|
〉 |