Statistica Sinica 11(2001), 537-547
EQUIVALENCE OF FRACTIONAL FACTORIAL DESIGNS
James B. Clark and A. M. Dean
Aerospace Corporation and The Ohio State University
Abstract:
Two designs for a fractional factorial experiment are
equivalent if one can be obtained
from the other by reordering the treatment combinations,
relabeling the factors and relabeling the factor levels. Designs
can be viewed as sets of points in 
-dimensional space, where
is
the number of factors. It is shown that, in this setting,
two designs are equivalent if the Hamming distances between the
points are the same in all possible dimensions.
An algorithm is given, based on this representation, that can detect
distinct designs for 
experiments
without a complete search of all
reorderings and relabelings in the fraction.
In addition, if two designs are equivalent, the algorithm gives a set of
permutations which map one design to the other.
Key words and phrases:
Design equivalence, fractional factorial experiment, Hamming distance.