Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.
@article{1117114341,
author = {Cheng, Ching-Shui and Tang, Boxin},
title = {A general theory of minimum aberration and its applications},
journal = {Ann. Statist.},
volume = {33},
number = {1},
year = {2005},
pages = { 944-958},
language = {en},
url = {http://dml.mathdoc.fr/item/1117114341}
}
Cheng, Ching-Shui; Tang, Boxin. A general theory of minimum aberration and its applications. Ann. Statist., Tome 33 (2005) no. 1, pp. 944-958. http://gdmltest.u-ga.fr/item/1117114341/