Designs for order-of-addition experiments.

Area of Science:

• Statistics
• Experimental Design
• Applied Mathematics

Background:

• Order-of-addition experiments are crucial for optimizing component sequences in diverse fields like biochemistry, food science, and pharmaceuticals.
• Despite its importance, the statistical methodology for order-of-addition studies remains underdeveloped.

Purpose of the Study:

• To develop a comprehensive statistical framework for pair-wise ordering designs.
• To introduce efficient methods for determining optimal component addition orders.
• To provide a benchmark for evaluating experimental designs in this area.

Main Methods:

• Development of a recursive relation for constructing full pair-wise ordering designs.
• Derivation of D-efficiency for the full pair-wise ordering model.
• Proposal of minimal-point pair-wise ordering designs to address cost constraints.

Main Results:

• A recursive method enables the generation of full pair-wise ordering designs without exhaustive evaluation.
• The D-efficiency benchmark aids in selecting appropriate fractional designs.
• Proposed minimal-point designs demonstrate high efficiency in practical applications.

Conclusions:

• The developed pair-wise ordering designs offer a statistically rigorous and efficient approach to optimizing addition sequences.
• These designs are valuable tools for researchers across various scientific disciplines seeking to optimize experimental outcomes.
• The study provides a foundational contribution to the statistical literature on order-of-addition experiments.