The Design of Order-of-Addition Experiments

TL;DR

This paper develops systematic methods for designing optimal order-of-addition experiments, creating new efficient designs and extending them to practical scenarios with process factors and restrictions.

Contribution

It introduces a framework for constructing optimal OofA designs using extended orthogonal arrays and provides new designs for various component counts.

Findings

Created 12-run OofA-OA designs for 4 and 5 components

Developed 24-run OofA-OA designs for 5 and 6 components

Extended designs to include process factors and ordering restrictions

Abstract

We 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 we investigate design fractions. Balance criteria for creating such designs employ an extension of orthogonal arrays (OA's) to OofA-OA's. A connection is made between $D$-efficient and OofA-OA designs. Necessary conditions are found for the number of runs needed to create OofA-OA's of strengths 2 and 3. We create a number of new, optimal, designs: 12-run OofA-OA's in 4 and 5 components, 24-run OofA-OA's in 5 and 6 components, and near OofA-OA's in 7 components. We extend these designs to include (a) process factors, and (b) the common case in which component orderings are restricted. We also suggest how such designs may be analyzed.