# The Design of Order-of-Addition Experiments

arXiv: https://arxiv.org/abs/1701.02786 · HTML: https://mlsanity.com/paper/1701.02786/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [Fast Approximation of the Shapley Values Based on Order-of-Addition Experimental Designs](https://mlsanity.com/paper/2309.08923/) (2023)

## Abstract (arXiv)

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.