Classical design structure of orthogonal designs with six to eight factors and sixteen runs
Article first published online: 20 DEC 2010
Copyright © 2010 John Wiley & Sons, Ltd.
Quality and Reliability Engineering International
Volume 27, Issue 1, pages 61–70, February 2011
How to Cite
Johnson, M. E. and Jones, B. (2011), Classical design structure of orthogonal designs with six to eight factors and sixteen runs. Qual. Reliab. Engng. Int., 27: 61–70. doi: 10.1002/qre.1170
- Issue published online: 27 JAN 2011
- Article first published online: 20 DEC 2010
- fractional factorial designs;
- projection properties;
- design generators;
- alias patterns
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 24 or a replicated 23 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.