Abstract: In many physical and computer experiments, the order in which the steps of a process are performed may have a substantial impact on the measured response. Often, the goal in these situations is to uncover the order that optimizes the response according to some metric. However, the brute force approach of performing all permutations quickly becomes impractical as the number of components in the process increases. Instead, we seek to develop order-of-addition experiments that choose an economically viable subset of permutations to test. The statistical literature on this topic is sparse, and many researchers rely on ad-hoc methods to study the effect of process order. In this work, we present a series of novel developments, including a modeling framework that exploits certain structures of the data, a method for constructing optimal designs under this proposed framework, and an evaluation of the performance and robustness of the constructed designs. We use data from a drug combination therapy problem to highlight the benefits of our approach.

Key words and phrases: Drug combination experiment, experimental design, generalized minimum aberration, Latin square, optimal design, orthogonal array.