This article discusses the optimal blocking criteria for nonregular two-level designs. We extend the optimal blocking criteria of Cheng and Wu to nonregular designs by adapting the G- and G 2-minimum aberration criteria discussed by Tang and Deng. To define word-length pattern for nonregular designs, we extend the notion of "word" to nonregular designs through a polynomial representation of factorial designs. We define treatment resolution and block resolution for evaluating the degrees of aliasing and confounding. We propose four new criteria, which we use to search for optimal blocking schemes of 12-run, 16-run, and 20-run two-level orthogonal arrays.
Bibliographical noteFunding Information:
The authors thank the editor, an associate editor, and two referees for valuable comments. This research was supported by the Supercomputing Institute for Digital Simulation and Advanced Computation at the University of Minnesota. S.-W. Cheng’s research was supported by the National Science Council of Taiwan, ROC. William Li’s research was supported by the Research And Teaching Supplement, Carlson School of Management, University of Minnesota. Part of Kenny Q. Ye’s research was conducted when he was a visiting research fellow at Academia Sinica, Taiwan, and his research is supported in part by National Science Foundation grant DMS-03-06306.
- Aliasing: Confounding
- Defining contrast subgroup
- Indicator function
- Orthogonal arrays
- Word-length pattern