Some properties of general minimum lower-order confounding designs

Abstract

The general minimum lower order confounding (GMC) criterion was proposed to select factorial designs, called GMC designs. The theory of constructing GMC 2^n–m designs with $5N/16+1\le n\le N-1$ was studied by Li, Zhao, and Zhang (2011), where 2^n–m denotes a two-level design with n factors and $N=2^{n-m}$ runs. In this article, we propose a method to study the properties of aliasing relations of GMC 2^n–m designs with $5N/16+1\le n\le N-1$, which make the aliasing information of these designs obtained theoretically. We illustrate how our method can be used to study partially GMC designs and blocked GMC designs.

Keywords:

• Aliased effect-number pattern
• blocked designs
• clear effects
• general minimum lower order confounding

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11501405, 11426161, 11601366, 11701088 and 11471239), the China Postdoctoral Science Foundation (Grant No. 2017M611147), and Tianjin “131” Talents Program.