NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

doi:10.1016/S0252-9602(16)30109-6

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (6): 1832-1840.doi: 10.1016/S0252-9602(16)30109-6

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NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

Shuo SONG¹, Qionghui ZHANG², Na ZOU³, Hong QIN²

1. College of Science, Wuhan University of Science and Technology, Wuhan 430065, China;
2. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
3. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received:2015-01-24 Revised:2016-05-03 Online:2016-12-25 Published:2016-12-25
Contact: Hong QIN,E-mail:qinhong@mail.ccnu.edu.cn E-mail:qinhong@mail.ccnu.edu.cn
Supported by:
The third author was supported by the National Natural Science Foundation of China (11301546). The fourth author is supported by the National Natural Science Foundation of China (11271147, 11471136).

Abstract

Abstract:

The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.

Key words: U-type design, Lee discrepancy, uniform design, lower bound

CLC Number:

62K15

Shuo SONG, Qionghui ZHANG, Na ZOU, Hong QIN. NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS[J].Acta mathematica scientia,Series B, 2016, 36(6): 1832-1840.

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NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

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