Statistica Sinica 14(2004), 203-215

ABERRATION, ESTIMATION CAPACITY

AND ESTIMATION INDEX

Hegang H. Chen$^1$ and Ching-Shui Cheng$^{2,3}$

$^1$University of Maryland School of Medicine,

$^2$Academia Sinica, Taipei and $^3$University of California, Berkeley

Abstract: Minimum aberration is a popular criterion for selecting fractional factorial designs. It aims at the minimization of aliasing among lower-order effects. Cheng, Steinberg and Sun (1999) showed that it is a good surrogate for maximum estimation capacity, a model robustness criterion, but they are not the same, especially for resolution IV designs. In this paper, the relationship between these two criteria is further investigated. The greater divergence of the two criteria on resolution IV designs is explained by the fact that a minimum aberration resolution III design can allocate all the available degrees of freedom to the estimation of two-factor interactions, while it is rarely so for resolution IV designs. A concept of estimation index is important in this regard.

Key words and phrases: Alias set, regular fractional factorial design, resolution, wordlength pattern.