A note on extending the alias length pattern

The alias length pattern (ALP) was proposed to characterize the aliasing among two-factor interactions for regular two-level fractional factorial designs of resolution I V . Experimenters often pay more attention to joint estimation of main effects and some two-factor interactions. Hence, resolution I I I and I V designs are commonly used in practice. In this article, we first extend the ALP for regular two-level fractional factorial designs of resolution I I I and I V by modeling justification. Then we study the properties of the ALP and provide the relationships between the ALP and other popular criteria.