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Computational Construction of Sequential Efficient Designs for the Second-Order Model

Author

Listed:
  • Norah Alshammari

    (School of Science, Royal Melbourne Institute of Technology University, Melbourne, VIC 3000, Australia
    Department of Mathematics, College of Science, University of Hail, Hail 2240, Saudi Arabia)

  • Stelios Georgiou

    (School of Science, Royal Melbourne Institute of Technology University, Melbourne, VIC 3000, Australia)

  • Stella Stylianou

    (School of Science, Royal Melbourne Institute of Technology University, Melbourne, VIC 3000, Australia)

Abstract

Sequential experimental designs enhance data collection efficiency by reducing resource usage and accelerating experimental objectives. This paper presents a model-driven approach to sequential Latin hypercube designs (SLHDs) tailored for second-order models. Unlike traditional model-free SLHDs, our method optimizes a conditional A-criterion to improve efficiency, particularly in higher dimensions. By relaxing the restriction of non-replicated points within equally spaced intervals, our approach maintains space-filling properties while allowing greater flexibility for model-specific optimization. Using Sobol sequences, the algorithm iteratively selects good points, enhancing conditional A-efficiency compared to distance minimization methods. Additional criteria, such as D-efficiency, further validate the generated design matrices, ensuring robust performance. The proposed approach demonstrates superior results, with detailed tables and graphs illustrating its advantages across applications in engineering, pharmacology, and manufacturing.

Suggested Citation

  • Norah Alshammari & Stelios Georgiou & Stella Stylianou, 2025. "Computational Construction of Sequential Efficient Designs for the Second-Order Model," Mathematics, MDPI, vol. 13(7), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1190-:d:1628040
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    References listed on IDEAS

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    1. David M. Steinberg & Dennis K. J. Lin, 2006. "A construction method for orthogonal Latin hypercube designs," Biometrika, Biometrika Trust, vol. 93(2), pages 279-288, June.
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    3. Pierre L’Ecuyer & Christiane Lemieux, 2002. "Recent Advances in Randomized Quasi-Monte Carlo Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 419-474, Springer.
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