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Classical design structure of orthogonal designs with six to eight factors and sixteen runs
Author(s) -
Johnson Mark E.,
Jones Bradley
Publication year - 2011
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1170
Subject(s) - fractional factorial design , plackett–burman design , mathematics , status quo , point (geometry) , column (typography) , arithmetic , factorial experiment , combinatorics , statistics , geometry , response surface methodology , connection (principal bundle) , economics , market economy
Most two‐level fractional factorial designs used in practice involve independent or fully confounded effects (so‐called regular designs). For example, for 16 runs and 6 factors, the classical resolution IV design with defining relation I = ABCE = BCDF = ADEF has become the de facto gold standard. Recent work has indicated that non‐regular orthogonal designs could be preferable in some circumstances. Inhibiting a wider usage of these non‐regular designs seems to be a combination of inertia/status quo and perhaps the general resistance and suspicion to designs that are computer generated to achieve ‘ X – Y – Z ’ optimality. In this paper each of the orthogonal non‐isomorphic two‐level, 16 run designs with 6, 7, or 8 factors (both regular and non‐regular) are shown to have a classical‐type construction with a 2 4 or a replicated 2 3 starting point. Additional factor columns are defined either using the familiar one‐term column generators or generators using weighted sums of effects. Copyright © 2010 John Wiley & Sons, Ltd.