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Order-of-Addition Orthogonal Arrays with High Strength

Author

Listed:
  • Shengli Zhao

    (School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China)

  • Zehui Dong

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China)

  • Yuna Zhao

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China)

Abstract

In order-of-addition experiments, the full order-of-addition designs are often unaffordable due to their large run sizes. The problem of finding efficient fractional OofA designs arises. The order-of-addition orthogonal arrays are a class of optimal fractional order-of-addition designs for the prevalent pair-wise ordering model, under a variety of widely used design criteria. In the literature, the studies on order-of-addition orthogonal arrays focused on strength 2 while the order-of-addition orthogonal arrays of higher strength have not been investigated yet. In this paper, we focus on order-of-addition orthogonal arrays of strength 3. First, the method of constructing order-of-addition orthogonal arrays of strength 3 is proposed. Second, a theoretical result that states that the order-of-addition orthogonal arrays of strength 3 have better balance properties than those of strength 2 is developed. Third, we provide thorough simulation studies which show that the constructed order-of-addition orthogonal arrays of strength 3 have desirable performance for estimating optimal orders of addition.

Suggested Citation

  • Shengli Zhao & Zehui Dong & Yuna Zhao, 2022. "Order-of-Addition Orthogonal Arrays with High Strength," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1187-:d:787227
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    References listed on IDEAS

    as
    1. Yuna Zhao & Zhiwei Li & Shengli Zhao, 2021. "A new method of finding component orthogonal arrays for order-of-addition experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 805-824, August.
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    3. 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).
    4. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    5. 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).
    6. T.C. Cheng & Guoqing Wang, 2000. "Single Machine Scheduling with Learning Effect Considerations," Annals of Operations Research, Springer, vol. 98(1), pages 273-290, December.
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