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Minimum $$\theta $$ θ -aberration criterion for designs with qualitative and quantitative factors

Author

Listed:
  • Liangwei Qi

    (Nankai University)

  • Yongdao Zhou

    (Nankai University)

Abstract

The minimum aberration criterion is popular for selecting good designs with qualitative factors under an ANOVA model, and the minimum $$\beta $$ β -aberration criterion is more suitable for selecting designs with quantitative factors under a polynomial model. However, numerous computer experiments involve both qualitative and quantitative factors, while there is a lack of a reasonable criterion to assess the effectiveness of such designs. This paper proposes some important properties of the $$\beta $$ β -wordlength pattern for mixed-level designs, and introduces the minimum $$\theta $$ θ -aberration criterion for comparing and selecting designs with qualitative and quantitative factors based on a full model involving all interactions of the factors. The computation of the $$\theta $$ θ -wordlength pattern is optimized by the generalized wordlength enumerator. Then we provide some construction methods for designs with less $$\theta $$ θ -aberration, and apply this criterion to screen the marginally coupled designs and the doubly coupled designs.

Suggested Citation

  • Liangwei Qi & Yongdao Zhou, 2025. "Minimum $$\theta $$ θ -aberration criterion for designs with qualitative and quantitative factors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(1), pages 99-117, January.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:1:d:10.1007_s00184-024-00951-7
    DOI: 10.1007/s00184-024-00951-7
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    References listed on IDEAS

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