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

Liangwei Qi () and Yongdao Zhou ()
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Liangwei Qi: Nankai University
Yongdao Zhou: Nankai University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 1, No 6, 99-117

Abstract: 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.

Keywords: Column-orthogonal; Fractional factorial design; Latin hypercube design; Orthogonal polynomial basis (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-024-00951-7

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