Some properties of .-wordlength pattern for four-level designs

Fractional factorial designs have played a prominent role in the theory and practice of experimental design. For designs with qualitative factors under an ANOVA model, the minimum aberration criterion has been frequently used; however, for designs with quantitative factors, a polynomial regression model is often established, thus the .-wordlength pattern can be employed to compare different fractional factorial designs. Although the .-wordlength pattern was introduced in 2004, its properties have not been investigated extensively. In this paper, we will present some properties of .-wordlength pattern for four-level designs. These properties can help find better designs with quantitative factors.