Page 272 - Six Sigma Demystified

252 Six SigMa DemystifieD

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Figure F.12 a 2 design.

tion terms with main factors, as shown in Table T.9. The result is a smaller de-
sign, a fraction of the original.
Consider the two-level three-factor CFD constructed earlier. It had 8 runs
to estimate the three main effects (A, B, and C), the three two-factor interac-
tions (AB, AC, and BC), and the one three-factor interaction (ABC). If we
assume that the ABC interaction is unlikely to be significant, then we can alias
it with a fourth factor D. The result of this alias is a design that is half the size!
Instead of requiring 16 runs, only 8 runs are needed to estimate the effect of
the four factors.
Construction of the four-factor FFD is similar to the three-factor design seen

earlier. The columns labeled “Factor A,” “Factor B,” and “Factor C” are identical
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to those shown in the CFD 2 design. The column labeled “Factor D” is con-
structed in the same way as its alias, the ABC interaction, is constructed—by
multiplying the columns for factors A, B, and C. For example, the first row, trial
1, is the result of multiplying (+ 1) × (+1) × (+1) = (+1).
Similarly,

Trial 2: (+1) × (+1) × (–1) = (–1)

Trial 3: (+1) × (–1) × (+1) = (–1)
Trial 4: (+1) × (–1) × (–1) = (+1)

And so on.