A Generalized General Minimum Lower Order Confounding Criterion for General Orthogonal Designs

Abstract

In this article, we extend the AENP and the GMC criterion proposed by Zhang et al. (2008) to the case of nonregular orthogonal designs. A G-AENP and correspondingly a G-GMC criterion are proposed. The confounding frequency vector (CFV) and the generalized wordlength pattern (GWLP), as the base of MGA and GMA criteria, are shown to be functions of the G-AENP. Some optimal properties of G-GMC designs are obtained. At the last, we give an efficient algorithm for finding optimal designs and tabulate some G-GMC designs with 16- and 18-run for application and comparison with GMA and MGA designs.

Keywords:

• Aliased effect-number pattern
• Confounding frequency vector
• GMA criterion
• GMC criterion
• Generalized wordlength pattern
• MGA criterion
• Nonregular orthogonal designs

Mathematics Subject Classification:

• Primary 62K15
• Secondary 62K05

Acknowledgments

The authors would like to thank the Associate Editor and referees for their valuable comments and structural suggestions for improving this article.

Additional information

Funding

This work was supported by the NNSF of China grant Nos. 11171165 and 10871104.