Deng and Tang proposed generalized resolution and minimum aberration
criteria for comparing and assessing nonregular fractional factorials, of which
Plackett–Burman designs are special cases.A relaxed variant of
generalized aberration is proposed and studied in this paper.We show that a
best design according to this criterion minimizes the contamination of
nonnegligible interactions on the estimation of main effects in the order of
importance given by the hierarchical assumption.The new criterion is defined
through a set of $B$ values, a generalization of word length pattern. We derive
some theoretical results that relate the $B$ values of a nonregular fractional
factorial and those of its complementary design. Application of this theory to
the construction of the best designs according to the new aberration criterion
is discussed. The results in this paper generalize those in Tang and Wu, which
characterize a minimum aberration (regular) $2^{m-k}$ design through its
complementary design.