  Nonregular fractional factorial designs such as Plackett-Burman designs and
other orthogonal arrays are widely used in various screening experiments for
their run size economy and flexibility. The traditional analysis focuses on
main effects only. Hamada and Wu (1992) went beyond the traditional approach
and proposed an analysis strategy to demonstrate that some interactions could
be entertained and estimated beyond a few significant main effects. Their
groundbreaking work stimulated much of the recent developments in design
criterion creation, construction and analysis of nonregular designs. This paper
reviews important developments in optimality criteria and comparison, including
projection properties, generalized resolution, various generalized minimum
aberration criteria, optimality results, construction methods and analysis
strategies for nonregular designs.
