Page 156 - Six Sigma Demystified

Chapter 6 a n a ly z e S tag e 137

significance. A line of significance, such as provided in Minitab software, pro-
vides the criteria for parameter selection. A normal or half- normal plot of the
effects provides similar results.
In this screening design, there were no extra runs to estimate error, so the
ANOVA table is of little value. Recall that at least one run (i.e., unique design
condition) is needed to estimate each parameter, including main effects (main
factors), their interactions, the overall mean (or intercept), and error. An
eight- run experiment can estimate at most seven factors and interactions. If
estimates are required for only six factors and interactions, then one run is avail-
able for estimating error. There are two choices to resolve this problem: Either
remove one or more of the required parameters from the analysis or add more
runs to the design. For example, the initial analysis in Figure 6.7 suggests that
the interaction AC (confounded with BD) is insignificant, so it is perhaps a
good candidate for removal. Removing it from the analysis would free up a run
to estimate error. Instead, this particular design was extended by folding the
design.
Folding the design is a technique for extending the design by repeating one
or more randomly selected runs or by replicating the entire design. In either
case, the additional trials should be run in random order and treated statistically
as a block (see “Factorial Designs” in Part 3). Of course, each additional run
increases the time and resources, and hence the cost, needed for the experi-
ment. On the other hand, each replicate also improves the ability to detect the
statistical significance of a given effect.
A design is folded by replicating the design and substituting the low values
with high values and the high values with low values for one or more of the
factors. If we fold on just one factor (i.e., substitute the plus and minus signs

for one of the factors), then that factor and its two- factor interactions will be
free of confounding. If we substitute the plus and minus signs for the entire
design, then all main factors will be free of confounding with other main factors
and two- factor interactions.
In this case, the design was extended by folding on the entire design. The
ANOVA table for the complete design is provided in Table 6.3. As described
in more detail in the “Regression Analysis” section of Part 3, the ANOVA table
provides an estimate of the regression significance (using the F statistic), pro-
vided that there is at least one extra run to calculate error. The regression for
2
this example is highly significant. The adjusted R value is 0.97, which indi-
cates that most of the variation in the data is accounted for by the regression
model.