Details of Research Outputs

Uniformity has played a key role in quasi-Monte Carlo methods as well as in computer experiments. The minimum aberration is the most popular criterion in factorial designs. In this paper we extend the results of Fang and Mukerjee (2000) from regular fractions of two-level factorials to regular fractions 3^s-1 of three-level factorials and establish a relationship between uniformity and aberration of regular fractions 3^s-1. There are many minimum aberration fractions 3^s-1 whose performances in statistical estimation may be different even though they are isomorphic to each other. Uniformity can be used as a criterion for comparing designs. A new concept of uniformly regular design is proposed. Construction of uniformly regular 3^s-1 designs is studied. We show that the uniformly minimum aberration 3^s-1 design has lower correlation and less confounding than the non-uniform one.