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A candidate-set-free algorithm for generating D-optimal split-plot designs.

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    A new method generates optimal split-plot designs efficiently, without needing a predefined candidate set. This computational approach is feasible for large experimental designs, improving statistical analysis.

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    Area of Science:

    • Statistics
    • Experimental Design
    • Industrial Engineering

    Background:

    • Split-plot designs are crucial for experiments with factors applied at different experimental levels.
    • Traditional methods for generating optimal split-plot designs often require large, computationally intractable candidate sets.
    • Efficiency in estimating fixed effects is paramount for accurate statistical modeling in complex experiments.

    Purpose of the Study:

    • To introduce a novel computational method for generating optimal split-plot designs.
    • To overcome the limitations of candidate set specification in split-plot design generation.
    • To provide a flexible and computationally feasible approach for creating efficient experimental designs.

    Main Methods:

    • A new algorithm for optimal split-plot design generation is presented.
    • The method does not require prior specification of a candidate set, enhancing computational feasibility.
    • It supports flexible sample sizes, continuous and categorical factors, and complex linear regression models.

    Main Results:

    • The proposed method successfully generates optimal split-plot designs.
    • It proves computationally feasible even for very large or intractable candidate sets.
    • A polypropylene experiment demonstrated a substantially more efficient design compared to existing approaches.

    Conclusions:

    • The new method offers a computationally efficient and flexible approach to generating optimal split-plot designs.
    • It expands the applicability of optimal design principles to complex experimental scenarios.
    • This advancement facilitates more accurate and efficient statistical analysis in various scientific and industrial fields.