Robust Design for Order-of-Addition Experiments

Order-of-addition experiment is a kind of experiment that considers the addition order of m components. Finding an effective design is crucial since the full design consisting of $m!$ permutations is unaffordable even for computer simulation. Several classes of designs have been proposed for certain models in recent years, but they may be singular under other models. In this article, we propose a robust design called maximin distance component orthogonal array whose minimum pairwise distance is maximized while the balance of any two columns from a component orthogonal array still holds. A genetic algorithm is used to search for such designs. The design, with excellent space-filling property, is robust since it is D-optimal under the component-position model and performs well under other models. A case study and an application show the good performance of the proposed design compared to the existing two classes of designs across many situations.