The Confounding Measure of Effects in Two-Level Regular Designs under Linear Model

In the design of experiments, the confounding of effects can cause the bias of parameter estimator in a linear model. This paper mainly proposes a confounding index for two-level regular designs to measure such bias. We introduce a new method to study the properties of the index and reveal the relationship between the confounding index, alias relation number, aliased component-number pattern, and word-length pattern. The confounding formula among lower-order effects is obtained to provide some conditions for optimal designs. Some examples are provided to illustrate the theoretical results.