Cheng, Ching-Shui; Tang, Boxin A general theory of minimum aberration and its applications. (English) Zbl 1068.62086 Ann. Stat. 33, No. 2, 944-958 (2005). Summary: Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question ist 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. 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.