An Aliasing Measure of Factor Effects in Three-Level Regular Designs

Area of Science:

• Statistics
• Experimental Design

Background:

• Confounding in three-level regular designs differs between factor and component effects.
• Factor effects' aliasing properties are more significant in experimental models.

Purpose of the Study:

• Propose a novel three-level aliasing pattern to quantify factor aliasing.
• Introduce a new criterion for selecting optimal three-level regular designs.

Main Methods:

• Developed a new classification pattern for aliasing.
• Introduced a new criterion for optimal design selection.
• Analyzed relationships between the new criterion and existing ones (e.g., minimum aberration).

Main Results:

• The proposed aliasing pattern and criterion provide a new way to evaluate factor aliasing.
• Existing criteria's classification patterns can be represented as functions of the proposed pattern.
• An aliasing algorithm and comprehensive design comparisons are presented.

Conclusions:

• The new aliasing pattern and criterion offer a unified approach to understanding and selecting three-level regular designs.
• This work provides a valuable tool for researchers in experimental design.