Construction of two-level component orthogonal arrays for order-of-addition experiments

Component orthogonal arrays (COAs), as subsets of all possible permutations on experimental factors, are suitable for designing order-of-addition experiments due to their pairwise balance property between any two positions of the orders. When the levels of components can be changed, the standard statistical design method has been to use the Cartesian product design, which often results in a large number of experimental runs. In this article, we consider combining COAs and 2(m-p) factional factorial designs by using a Subcartesian product. A systematic method is given for design construction. In the construction method, both the COA and 2(m-p) design are sliced properly, and then the two designs are combined by the Subcartesian product. We show that the number of runs obtained by the Subcartesian product method is usually much smaller than that obtained by the Cartesian product method. In addition, the constructed design satisfies the pairwise balance property and has the same D-efficiency as the full m! x 2(m) design under the main-effect model. Examples are given to illustrate the proposed method.