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Minimum aberration and model robustness for two‐level fractional factorial designs
Author(s) -
Cheng C.S.,
Steinberg D. M.,
Sun D. X.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00164
Subject(s) - fractional factorial design , robustness (evolution) , mathematics , alias , factorial experiment , plackett–burman design , algorithm , mathematical optimization , computer science , statistics , data mining , biochemistry , chemistry , response surface methodology , gene
The performance of minimum aberration two‐level fractional factorial designs is studied under two criteria of model robustness. Simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived. It is also shown that a minimum aberration design of resolution III or higher maximizes the number of two‐factor interactions which are not aliases of main effects and, subject to that condition, minimizes the sum of squares of the sizes of alias sets of two‐factor interactions. This roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform. It follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here. Examples are given to show that minimum aberration designs are indeed highly efficient.