Recent developments in nonregular fractional factorial designs

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 optimality criteria, construction and analysis of nonregular designs. This paper reviews important developments in nonregular designs, including projection properties, generalized resolution, generalized minimum aberration criteria, optimality results, construction methods and analysis strategies.