A Component-Position Model, Analysis and Design for Order-of-Addition Experiments

An order-of-addition experiment is a kind of experiment in which the response is affected by the addition order of materials or components. In many situations, performing the full design with all possible permutations of components is unaffordable, especially when the number of components is larger than four. We introduce a component-position model for analyzing data from such experiments and study associated problems. We further propose a new type of design, called component orthogonal array, as a fraction of the full design for order-of-addition experiments. It is shown that component orthogonal arrays have the same D-efficiency as the full design under our proposed model. Component orthogonal arrays also perform well under the existing pairwise ordering model. Two drug combination experiments are used to show the effectiveness of the proposed model and designs. Supplementary materials for this paper are available online.