Recent Developments in Nonregular Fractional Factorial Designs

TL;DR

This paper reviews recent advances in the theory, construction, and analysis of nonregular fractional factorial designs, emphasizing optimality criteria, projection properties, and strategies for estimating effects beyond main effects.

Contribution

It provides a comprehensive overview of recent developments in optimality criteria, construction methods, and analysis strategies for nonregular fractional factorial designs.

Findings

Enhanced understanding of projection properties and generalized resolution.

Development of new optimality criteria and construction methods.

Improved analysis strategies for nonregular 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 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.