Optimal confounding measures for two-level regular designs

Abstract

The aliased effect-number pattern is usually used to reveal the confounding distributions between various factorial effects in any two-level regular design. However, it does not reflect all the confounding information’s properties of concentricity and variation. The article proposes the concepts of confounding average and variance to solve the problem and introduce optimal confounding measures. We further study the relationship between the confounding average, resolution, and word length pattern. Finally, compared with other criteria, optimal designs with 16, 32, and 64 runs are tabulated under confounding measures.

KEYWORDS:

• Regular design
• aliased effect-number pattern
• confounding average
• confounding variance

Mathematics Subject Classification:

• 62K15
• 62K05

Acknowledgments

We thank editors and reviewers for constructive and valuable advice for improving this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China (12061070) and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (2021D01E13).