Page 276 - Six Sigma Demystified

256 Six SigMa DemystifieD

Interpretation

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The two-levels-per-factor (2 ) designs used for screening only can provide a
first-order model. When saturated designs have been augmented with one or
more additional runs, we can estimate the error in the model and the signifi-
cance of parameters using ANOVA techniques “Regression” topic outlined ear-
lier. Error in a regression analysis is due to two sources—pure error and
lack-of-fit error. Pure error is experimental error, the differences between re-
peated runs of the same condition. The remaining error is due to a poor fit of
the model to the data. Error owing to a lack of fit is caused by either a curvature
in the response surface that is not estimated with the fitted first-degree model
or main factor or interaction terms not included in the model. When center
points are available, the F statistic may be used to investigate curvature in the
data, suggesting the need for a higher-order model. (This technique is explained
further under “Response Surface Analysis” below.)
The parameter effects, the influence each factor or interaction has on the
response, can be estimated for the 2 design by calculating the difference
k
between the average response when the parameter is set at the high level and
the average response when the parameter is set at the low level. The coefficient
of the parameter in the regression model is calculated as one-half the effect.
In the fractional factorial 2 design, the effect of the aliasing is confounding
k–x
between main factors and interactions. For example, if an FFD is run where
factor A and interaction BC are confounded, then the calculated parameter
effect may be due to either factor A, the interaction BC, or a linear combination
of factor A and interaction BC.
When the results of a screening experiment are ambiguous because of the
confounding of factors, we often can fold the design to select additional trials to

remove the confounding. A design is folded by replicating the design and sub-
stituting the low levels with high levels and high values with low levels 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 interac-
tions 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.
The next step after successful analysis of the screening experiment depends
on the objectives of the experimental process.

• To control the process, the successful experiment has differentiated be-
tween the significant and insignificant sources of variation. Verify by rep-