  Minimum aberration is an increasingly popular criterion for comparing and
assessing fractional factorial designs, and few would question its importance
and usefulness nowadays. In the past decade or so, a great deal of work has
been done on minimum aberration and its various extensions. This paper develops
a general theory of minimum aberration based on a sound statistical principle.
Our theory provides a unified framework for minimum aberration and further
extends the existing work in the area. More importantly, the theory offers a
systematic method that enables experimenters to derive their own aberration
criteria. Our general theory also brings together two seemingly separate
research areas: one on minimum aberration designs and the other on designs with
requirement sets. To facilitate the design construction, we develop a
complementary design theory for quite a general class of aberration criteria.
As an immediate application, we present some construction results on a weak
version of this class of criteria.
