Some Porperties of Aliased Component-Number Pattern for Regular Fractional Factorial Designs

General minimum lower-order confounding and minimum aberration are two important criteria to select s\,(s\geq 2)-level optimal regular fractional factorial designs. Their classification are based on the aliased component-number and word-length patterns, respectively. The paper mainly studies some properties of the aliased component-number pattern for s-level regular designs. We obtain that the elements of word-length pattern are expressed as some functions of aliased component-numbers under s-level case. It reveals the relationship between the aliased component-number and word-length patterns. On the other hand, we can calculate some aliased component-numbers by word-length pattern. Further, the formulas of some aliased component-numbers are provided for two-level designs.