Design of Order-of-Addition Experiments

TL;DR

This paper develops a theoretical framework for designing efficient order-of-addition experiments, establishing optimality of uniform designs and proposing robust fractional designs to improve experimental efficiency.

Contribution

It introduces a broad model for order-of-addition experiments, proves the optimality of uniform designs under this model, and constructs robust fractional designs for practical use.

Findings

Uniform design measure is optimal under the model.

Eigen-analysis provides a benchmark for design efficiency.

A closed-form construction of robust fractional designs is proposed.

Abstract

In an order-of-addition experiment, each treatment is a permutation of m components. It is often unaffordable to test all the m! treatments, and the design problem arises. We consider a model that incorporates the order of each pair of components and can also account for the distance between the two components in every such pair. Under this model, the optimality of the uniform design measure is established, via the approximate theory, for a broad range of criteria. Coupled with an eigen-analysis, this result serves as a benchmark that paves the way for assessing the efficiency and robustness of any exact design. The closed-form construction of a class of robust optimal fractional designs is then explored and illustrated.