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<p>Discrepancy is an important criterion for measuring the uniformity of designs. In this paper, the uniformity of mixed-level designs with random errors in the factor levels is studied under the wrap-around <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_2\)</EquationSource> </InlineEquation>-discrepancy. Given a mixed-level design, the expectation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(B_z\)</EquationSource> </InlineEquation> of the difference between wrap-around <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L_2\)</EquationSource> </InlineEquation>-discrepancies of the mixed-level design with and without random errors in the factor levels is defined, and the properties of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(B_z\)</EquationSource> </InlineEquation>, along with its upper and lower bounds are studied. Numerical examples and simulation for Goldstein-Price function model demonstrate that uniform designs performs robustly against interferences with random errors in the factor levels.</p>

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Mixed-level uniform design with random errors in the level values

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Jianliang Guo,
  • Zujun Ou,
  • Ling He

摘要

Discrepancy is an important criterion for measuring the uniformity of designs. In this paper, the uniformity of mixed-level designs with random errors in the factor levels is studied under the wrap-around \(L_2\) -discrepancy. Given a mixed-level design, the expectation \(B_z\) of the difference between wrap-around \(L_2\) -discrepancies of the mixed-level design with and without random errors in the factor levels is defined, and the properties of \(B_z\) , along with its upper and lower bounds are studied. Numerical examples and simulation for Goldstein-Price function model demonstrate that uniform designs performs robustly against interferences with random errors in the factor levels.