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Area of Science:

  • Experimental Design
  • Statistical Modeling
  • Applied Mathematics

Background:

  • Contemporary experiments frequently utilize branching and nested factors.
  • Existing design criteria often neglect the space-filling properties of low-dimensional projections.
  • This oversight can reduce design efficiency, particularly when few factors are significant.

Purpose of the Study:

  • To propose a novel space-filling criterion for evaluating designs with branching and nested factors.
  • To develop a framework for constructing optimal designs based on this new criterion.
  • To improve the performance of experimental designs in terms of space-filling properties.

Main Methods:

  • A new space-filling criterion is proposed, building upon the maximum projection criterion.
  • A framework for constructing optimal designs under the proposed criterion is developed.
  • The method evaluates designs based on low-dimensional projections.

Main Results:

  • The proposed criterion offers superior space-filling properties across all low-dimensional projections compared to existing methods.
  • The developed framework successfully constructs optimal designs.
  • The new designs demonstrate enhanced performance, especially when dealing with complex factor structures.

Conclusions:

  • The novel space-filling criterion and construction framework provide a significant advancement for experimental designs with branching and nested factors.
  • The resulting designs exhibit improved space-filling properties, leading to more robust and efficient experiments.
  • The strategy's broad applicability is highlighted by its lack of constraints on run size, factor levels, or factor types.