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<p>In many industrial applications, the factors of the designs may include qualitative (nominal or ordinal) and quantitative (continuous or discrete) factors. However, existing criteria for measuring the uniformity of such designs have certain limitations. To address this issue, this paper proposes a new uniformity criterion, called the general discrepancy (GD), to measure the uniformity of the designs, including qualitative (nominal or ordinal) and quantitative (continuous or discrete) factors. Furthermore, a closed-form expression for the novel discrepancy is derived, which allows the GD value of any design to be directly calculated. This makes it possible to accurately and efficiently compare the uniformity of different designs. We also establish the relationship between the GD and the balance pattern, thereby providing statistical justification for the GD. Additionally, we derive three tight lower bounds for directly identifying uniform designs and demonstrate their achievability through numerical examples. Finally, by fitting the statistical surrogate models, uniform designs based on the GD criterion achieve better prediction performance over the competing method.</p>

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A general discrepancy for experimental designs with multiple factor types

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Chunyan Wen,
  • Yunxi Yang,
  • Feng Yang

摘要

In many industrial applications, the factors of the designs may include qualitative (nominal or ordinal) and quantitative (continuous or discrete) factors. However, existing criteria for measuring the uniformity of such designs have certain limitations. To address this issue, this paper proposes a new uniformity criterion, called the general discrepancy (GD), to measure the uniformity of the designs, including qualitative (nominal or ordinal) and quantitative (continuous or discrete) factors. Furthermore, a closed-form expression for the novel discrepancy is derived, which allows the GD value of any design to be directly calculated. This makes it possible to accurately and efficiently compare the uniformity of different designs. We also establish the relationship between the GD and the balance pattern, thereby providing statistical justification for the GD. Additionally, we derive three tight lower bounds for directly identifying uniform designs and demonstrate their achievability through numerical examples. Finally, by fitting the statistical surrogate models, uniform designs based on the GD criterion achieve better prediction performance over the competing method.