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Some properties of \(\beta\)-wordlength pattern for four-level designs. (English) Zbl 1317.62062

Summary: 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 \(\beta\)-wordlength pattern can be employed to compare different fractional factorial designs. Although the \(\beta\)-wordlength pattern was introduced in 2004, its properties have not been investigated extensively. In this paper, we will present some properties of \(\beta\)-wordlength pattern for four-level designs. These properties can help find better designs with quantitative factors.

MSC:

62K15 Factorial statistical designs
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