Stratum order-of-addition designs

Liushan Zhou, Ze Liu, Min-Qian Liu, Guanzhou Chen

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · Mon

Abstract

Order-of-addition experiments are widely employed in many fields of science and industry to study how the order of components being added influences the response. Although several classes of attractive order-of-addition designs have been proposed in recent years, the performance of these designs often relies on prespecified models and their run sizes are typically large unless the number of components is very small. In this paper, we put forward a model-free approach, calledstratum order-of-addition designs, for order-of-addition experiments. By achievingstratum orthogonalityof various strengths, the proposed designs are not only economical in run size, but also robust to model uncertainty. Theoretical justifications for these designs are established under a broad class of models for order-of-addition experiments. In addition, several deterministic methods are developed for constructing such designs with flexible run sizes. Numerical studies demonstrate that the proposed designs are competitive under many model-based and model-free criteria, as compared with existing designs in the literature.

Keywords

component orthogonal array, orthogonal array, space-filling design, stratified component-position model, stratum orthogonality

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