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Order-of-addition experiments with order constraints

Author

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  • Xinran Zhang

    (Nankai University)

  • Liuqing Yang

    (Central South University)

  • Jian-Feng Yang

    (Nankai University)

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.

Suggested Citation

  • Xinran Zhang & Liuqing Yang & Jian-Feng Yang, 2025. "Order-of-addition experiments with order constraints," Statistical Papers, Springer, vol. 66(6), pages 1-32, October.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:6:d:10.1007_s00362-025-01752-4
    DOI: 10.1007/s00362-025-01752-4
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    References listed on IDEAS

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    1. Chen, Jianbin & Mukerjee, Rahul & Lin, Dennis K.J., 2020. "Construction of optimal fractional Order-of-Addition designs via block designs," Statistics & Probability Letters, Elsevier, vol. 161(C).
    2. Wei Wei, 2019. "Single machine scheduling with stochastically dependent times," Journal of Scheduling, Springer, vol. 22(6), pages 677-689, December.
    3. Zhao, Yuna & Lin, Dennis K.J. & Liu, Min-Qian, 2022. "Optimal designs for order-of-addition experiments," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
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