Analysis and Construction of Nonregular Fractional Factorial Designs

Abstract

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 exibility. 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. In the first part of this talk, I provide new real-life examples to show the necessarity of considering significant interactions. Data are reanalyze in these examples with the consideration of interactions via both a frequentist and a Bayesian approach. In the second part of this talk, I discuss the construction of optimal nonregular designs. We focus on a class of nonregular designs constructed via quaternary codes and completely characterize the structure of quarter-fraction factorial designs. Then we construct optimal designs under the maximum resolution, minimum aberration and maximum projectivity criteria. We further prove that some of these designs are optimal among all possible designs.