Uniform Experimental Design Strategies in Statistical Analysis

Uniform experimental designs are a class of space-filling arrangements that seek to distribute experimental runs as evenly as possible throughout the factor space. They rely on quantitative measures of uniformity, most commonly centred L2-discrepancy and weighted variants, to assess how closely the design points approximate a perfectly uniform distribution. Such strategies are essential in computer experiments, simulation studies and screening trials where the goal is to explore complex response surfaces without bias or clustering. Uniform designs extend classical factorial and orthogonal array approaches by accommodating mixed-level factors and higher dimensions while preserving desirable projection properties. Recent advances have linked uniformity measures to design-efficiency criteria, enabling practitioners to select compact yet informative designs through optimisation algorithms. Their global significance is evident across disciplines—from materials science to systems biology—where robust coverage of input spaces underpins reliable model building and parameter tuning.

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Technical terms

Discrepancy: A numerical index that quantifies the deviation of design points from an ideal uniform distribution in the experimental region.

Uniform design: An experimental arrangement chosen to minimise discrepancy, ensuring even coverage of the factor space.

Fractional factorial design: A subset of all possible combinations of factor levels, selected to estimate main effects and lower-order interactions efficiently.

Orthogonal array: A matrix of factor levels in which columns are arranged so that all level combinations for any subset of factors occur with equal frequency.

Mixed-level design: An experimental design in which different factors may have differing numbers of levels.

Projection uniformity: The uniformity of a design’s marginal distributions when projected onto a lower-dimensional subspace of factors.

References

1. Design Efficiency of the Asymmetric Minimum Projection Uniform Designs. Mathematics (2023).
2. Direct Constructions of Uniform Designs under the Weighted Discrete Discrepancy †. Axioms (2022).
3. Projection Uniformity of Asymmetric Fractional Factorials. Axioms (2022).