Page 273 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 253

TAble T.9 a Fractional Factorial Design for Four Factors

Std. Order Factor A Factor B Factor C Factor D
1 + + + +
2 + + – –
3 + – + –
4 + – – +
5 – + + –
6 – + – +
7 – – + +
8 – – – –

The effect of aliasing factor D with the ABC interaction is that the aliased
parameters are confounded with one another. This implies that the parameters
cannot be estimated independently of one another. For example, if factor D is
aliased with the ABC interaction, then when the effect of factor D is estimated,
we cannot be sure whether the effect is due to factor D, the ABC interaction,
or a linear combination of D and ABC.
The intended aliasing also creates some unintended confounding between all
the other possible combinations of the aliased pair. We construct the con-
founded pairs by moving the equal sign through the ABC = D equation. If ABC
= D, then A = BCD; B = ACD; C = ABD; AB = CD; AC = BD; and AD =
BC.These can be verified in Table T.9 by noticing, for example, that the results
of multiplying the columns for factor A and factor B provide the same result
for all rows as multiplying the columns for factor C and factor D. This provides

evidence that the AB interaction is confounded with the CD interaction.
FFDs have several uses. They are used commonly as screening designs to
identify significant factors and their interactions and to remove insignificant
factors and interactions. We often start the design process with many factors,
brainstorm to a manageable number of key factors, and then run a relatively
small screening design to reduce the number of factors and interactions even
further. This allows further designs to explore the process dynamics in more
detail, using fewer factors in the model.
FFDs are also used in response surface analysis to develop the initial first-
order model and its factor effect estimates needed for the steepest ascent meth-
ods. When higher-order models are suspected, the FFDs can be supplemented
with axial and center points.