Some Results on Fractional Factorial Split-Plot Designs with Multi-Level Factors

Abstract

Fractional factorial split-plot (FFSP) designs have received much attention in recent years. In this article, the matrix representation for FFSP designs with multi-level factors is first developed, which is an extension of the one proposed by Bingham and Sitter (1999b) for the two-level case. Based on this representation, periodicity results of maximum resolution and minimum aberration for such designs are derived. Differences between FFSP designs with multi-level factors and those with two-level factors are highlighted.

Keywords:

• Fractional factorial design
• Maximum resolution
• Minimum aberration
• Split-plot design

Mathematics Subject Classification:

• Primary 62K15
• Secondary 62K05

Acknowledgments

The authors cordially thank Professor Rahul Mukerjee for his valuable suggestions, the Chief Editor, an Associate Editor, and the referees for their detailed comments. This work was supported by the Program for New Century Excellent Talents in University (NCET-07-0454) of China, the NNSF of China Grants 10571093 and 10671099, and the SRFDP of China Grant 20050055038.