Lower Bounds for the Uniformity Pattern of Asymmetric Fractional Factorials

Abstract

The objective of this article is to study the issue of the projection discrepancy (Fang and Qin, 2005; Ma et al. 2003), which has wide application to the field of fractional factorials. Fang and Qin (2005) and Zhang and Qin (2006) derived some properties of the projection properties of two-level factorials. Here we extend their results to asymmetric factorials. Some lower bounds of projection discrepancy of asymmetrical factorials are also obtained.

Keywords:

• Asymmetrical fractional factorial
• Lower bound
• Projection discrepancy

Mathematics Subject Classification:

• Primary 62K15
• Secondary 62K05

Acknowledgments

The authors would like to thank the referee and Chief Editor for their valuable comments and suggestions that lead to the improvement in the presentation of the article. This research was partially supported by the NNSF of China (No. 10671080), NCET (No. 06-672), and the Key Project of Chinese Ministry of Education (No. 105119).