Page 155 - Six Sigma Demystified

136 Six SigMa DemystifieD

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. When factor D is aliased
with the ABC interaction, when we estimate the effect of factor D, we cannot
be sure whether the effect is due to factor D, the ABC interaction, or a linear
combination of the main factor D and the three- factor ABC interaction.
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; AD = BC

Thus this eight- run experiment will estimate each of the main factors A, B, C,
and D, each of which will be confounded with a three- factor interaction and
the 6 two- factor interactions (confounded with each other). The analysis pro-
vided by this experiment is scant because there are no additional runs added
for estimating error. An effects plot, shown in Figure 6.7, displays the absolute
value of the (coded) effects in a Pareto chart. Larger coded effects have higher

Figure­6.7 Pareto chart of effects showing significance of factor B.