Optimal Two-Level Fractional Factorial Designs for Location Main Effects with Dispersion Factors

Abstract

In two-level fractional factorial designs, homogeneous variance is commonly assumed in analysis of variance. When the variance of the response variable changes when a factor changes from one level to another, we call that factor the dispersion factor. However, the problem of finding optimal designs when dispersion factors are present is relatively unexplored. In this article, we focus on finding optimal designs for the estimation of all location main effects when there are one or two dispersion factors, in the class of regular single replicated two-level fractional factorial designs of resolution III or higher. We show that by appropriate naming of the dispersion factors, D-optimal and A-optimal designs can be identified. Table of D-optimal resolution III designs with two dispersion factors is given.

Keywords:

• A-optimality
• D-optimality
• Dispersion effect
• Location effects

Mathematics Subject Classification:

• Primary 62K05
• Secondary 62K15

Acknowledgments

We wish to thank the reviewer for many helpful comments that improved the manuscript. This work is supported by the National Science Council Taiwan, grant number NSC96-2118-M-004-005.