Order-of-addition experiments for sequential adjacency relationship problems

Order-of-addition (OofA) experiments are widely utilized in diverse fields, such as industry and pharmacy. The two most commonly employed models are the pairwise ordering model and the component-position model. However, in certain experimental problems, the response only depends on the adjacency relationship (AR) between components, rather than their absolute or relative positions. This is referred to as the AR problem. Among the different types of AR problems, spatial AR and sequential AR are frequently discussed, yet research on sequential AR remains rather limited. In this paper, we introduce OofAM, a method grounded in OofA experiments to tackle the sequential AR problem. The proposed method encompasses a novel model, designs with certain theoretical properties, along with some analytical techniques for inferring the optimal orders. As a first attempt to apply OofA experiments to solve the sequential AR problem, OofAM is both straightforward and information-efficient. Moreover, case studies demonstrate that the proposed method outperforms other methods in terms of efficiency, especially for large-scale problems.