Order-of-addition experiments with order constraints

Xinran Zhang, Liuqing Yang and Jian-Feng Yang ()
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Xinran Zhang: Nankai University
Liuqing Yang: Central South University
Jian-Feng Yang: Nankai University

Statistical Papers, 2025, vol. 66, issue 6, No 9, 32 pages

Abstract: Abstract In numerous scenarios, the sequence in which components or materials are added can have a substantial impact on the experimental outcomes. This concept, known as order-of-addition experiments, has been the subject of extensive research. Previous studies predominantly focus on these experiments under unconstrained conditions, allowing each component to be placed in any position within the addition sequence. However, in practical applications, especially in fields such as the transportation industry and food science, specific ordering of components often becomes a necessity. This paper delves into order-of-addition experiments with order constraints, where certain components must be added prior to others. We provide the corresponding constrained models and experimental designs. For single order constraints, where one component should precede another, we show the optimality of the constrained full design. Additionally, we introduce a construction method for optimal fractional designs, which can remarkably reduce the number of experimental runs. Furthermore, for multiple order constraints, where one set of components must be added before another set, we present a construction method for optimal fractional designs along with an analysis of their properties. Moreover, we also consider other types of multiple order constraints, offering a comprehensive overview and algorithmic support for the efficient search of fractional designs.

Keywords: Bubble sort algorithm; Optimal design; Order-of-addition orthogonal array; Pairwise ordering model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01752-4

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