Hamming Weight Uniform Designs for Order-of-Addition Experiments

Order-of-addition (OofA) designs study systems where outcomes depend on the sequences of components. Existing designs often rely on specific parametric models, leading to fragile inference when models are misspecified. This paper bridges the methodological gap in model-robust OofA design by introducing Hamming weight as a novel uniformity metric. Theoretical properties of Hamming weight distributions within the full designs are established, enabling the efficient construction of Hamming weight uniform designs (HWUDs). HWUDs ensure estimator consistency, maintain asymptotic equivalence to full designs, and deliver robust performance across diverse models. Additionally, HWUDs provide a design-based, model-robust framework for channel attribution problems. Empirical results on real-world data demonstrate that HWUDs achieve substantial improvements in both statistical accuracy and computational efficiency over current approaches.