Maxpro Designs for Experiments with Multiple Types of Branching and Nested Factors

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.