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Theory of optimal blocking of nonregular factorial designs
Author(s) -
Al Mingyao,
Zhang Runchu
Publication year - 2004
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315999
Subject(s) - fractional factorial design , factorial experiment , mathematics , factorial , blocking (statistics) , block (permutation group theory) , coding theory , type (biology) , coding (social sciences) , orthogonal array , block design , plackett–burman design , designtheory , arithmetic , mathematical optimization , computer science , discrete mathematics , combinatorics , statistics , mathematical analysis , ecology , response surface methodology , human–computer interaction , taguchi methods , biology
The authors introduce the notion of split generalized wordlength pattern (GWP), i.e., treatment GWP and block GWP, for a blocked nonregular factorial design. They generalize the minimum aberration criterion to suit this type of design. Connections between factorial design theory and coding theory allow them to obtain combinatorial identities that govern the relationship between the split GWP of a blocked factorial design and that of its blocked consulting design. These identities work for regular and nonregular designs. Furthermore, the authors establish general rules for identifying generalized minimum aberration (GMA) blocked designs through their blocked consulting designs. Finally they tabulate and compare some GMA blocked designs from Hall's orthogonal array OA (16,2 1 5,2) of type III.