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 IV. Experimenters often pay more attention to joint estimation of main effects and some two-factor interactions. Hence, resolution III and IV designs are commonly used in practice. In this article, we first extend the ALP for regular two-level fractional factorial designs of resolution III and IV by modeling justification. Then we study the properties of the ALP and provide the relationships between the ALP and other popular criteria.