The minimum aberration criterion is popular for selecting good designs with qualitative factors under an ANOVA model, and the minimum \(\beta \) -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 \(\beta \) -wordlength pattern for mixed-level designs, and introduces the minimum \(\theta \) -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 \(\theta \) -wordlength pattern is optimized by the generalized wordlength enumerator. Then we provide some construction methods for designs with less \(\theta \) -aberration, and apply this criterion to screen the marginally coupled designs and the doubly coupled designs.
