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Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors

Author

Listed:
  • Meng-Meng Liu

    (School of Science, Minzu University of China, Beijing 100081, China
    These authors contributed equally to this work.)

  • Min-Qian Liu

    (NITFID, LPMC & KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin 300071, China
    These authors contributed equally to this work.)

  • Jin-Yu Yang

    (NITFID, LPMC & KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin 300071, China
    These authors contributed equally to this work.)

Abstract

Computer experiments often involve both qualitative and quantitative factors, posing challenges for efficient experimental designs. Strongly coupled designs (SCDs) are proposed in this paper to balance flexibility in run size and stratification properties between qualitative and quantitative factor columns. The existence and construction of SCDs are investigated. When s ⩾ 2 is a prime or a prime power, the constructed SCDs of λ s 3 runs can accommodate 2 s − 1 qualitative factors and a substantial number of quantitative factors. Furthermore, a series of SCDs with s u rows and ( u − 3 ) s 3 columns of quantitative factors are constructed, where u ⩾ 4 , with certain columns of quantitative factors achieving stratification in two or higher dimensions. The proposed SCDs achieve stratification between any two qualitative factors and all quantitative factors, which is superior to MCDs. With the number of levels of the qualitative factors given as s 2 , DCDs have λ s 4 rows, while SCDs have only λ s 3 rows, offering more flexibility. Furthermore, in the designs constructed in this paper with fewer than 100 rows, in 11 out of 17 cases, SCDs have a larger number and higher levels of qualitative factors than DCDs.

Suggested Citation

  • Meng-Meng Liu & Min-Qian Liu & Jin-Yu Yang, 2024. "Strongly Coupled Designs for Computer Experiments with Both Qualitative and Quantitative Factors," Mathematics, MDPI, vol. 13(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:75-:d:1555458
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    References listed on IDEAS

    as
    1. Yongdao Zhou & Boxin Tang, 2019. "Column-orthogonal strong orthogonal arrays of strength two plus and three minus," Biometrika, Biometrika Trust, vol. 106(4), pages 997-1004.
    2. Yuanzhen He & Boxin Tang, 2013. "Strong orthogonal arrays and associated Latin hypercubes for computer experiments," Biometrika, Biometrika Trust, vol. 100(1), pages 254-260.
    3. Weiping Zhou & Jinyu Yang & Min-Qian Liu, 2021. "Construction of orthogonal marginally coupled designs," Statistical Papers, Springer, vol. 62(4), pages 1795-1820, August.
    4. Weiping Zhou & Shigui Huang & Min Li, 2024. "Group Doubly Coupled Designs," Mathematics, MDPI, vol. 12(9), pages 1-21, April.
    Full references (including those not matched with items on IDEAS)

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