Some results on constructing two-level block designs with general minimum lower order confounding

ABSTRACT

Block designs are widely used in experimental situations where the experimental units are heterogeneous. The blocked general minimum lower order confounding (B-GMC) criterion is suitable for selecting optimal block designs when the experimenters have some prior information on the importance of ordering of the treatment factors. This paper constructs B-GMC 2^{n − m}: 2^r designs with 5 × 2^l/16 + 1 ⩽ n − (N − 2^l) < 2^{l − 1} for l(r + 1 ⩽ l ⩽ n − m − 1), where 2^{n − m}: 2^r denotes a two-level regular block design with N = 2^{n − m} runs, n treatment factors, and 2^r blocks. With suitable choice of the blocking factors, each B-GMC block design has a common specific structure. Some examples illustrate the simple and effective construction method.

KEYWORDS:

• Aliased effect-number pattern
• effect hierarchy principle
• minimum lower order confounding
• resolution
• Yates order.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K15
• 62K05

Acknowledgments

The authors thank the associate editor and the referees for their valuable comments and structural suggestions for improving the paper.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 11371223]; Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province; Program for Scientific Research Innovation Team in Applied Probability and Statistics of Qufu Normal University [grant number 0230518]; and the Scientific and Technological Program of Qufu Normal University [grant number xkj201519].