The design of order-of-addition experiments

Abstract

I introduce systematic methods to create optimal designs for order-of-addition (OofA) experiments, those that study the order in which m components are applied—for example, the order in which chemicals are added to a reaction or layers are added to a film. Full designs require m! runs, so I investigate design fractions. Balance criteria for creating such designs employ an extension of orthogonal arrays (OAs) to OofA–OAs. A connection is made between D-efficient and OofA–OA designs. Necessary conditions are found for the number of runs needed to create OofA–OAs of strengths 2 and 3. I create a number of new, optimal, designs: 12-run OofA–OAs in 4 and 5 components, 24-run OofA–OAs in 5 and 6 components, and near OofA–OAs in 7 components. I extend these designs to include (a) process factors and (b) the common case in which component orderings are restricted. I also suggest how such designs may be analyzed.

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