Page 290 - Six Sigma Demystified

270 Six SigMa DemystifieD

by the pencil, then the data fit the distribution fairly well. The statistical goodness-
of-fit tests described here obviously add objectivity to the analysis.
The adequacy of the test for a given distributional fit depends on the stability
of the process and the number of data points. Generally, 200 to 300 data points
are recommended for testing distributional fits, although fewer data points can
be used with less certainty in the results. If the process is not in statistical con-
trol, then no one distribution should be fit to the data.

Methodology

The K-S criterion is based on the expectation that there is likely to be a differ-
ence between a discrete distribution generated from data and the continuous
distribution from which the data were drawn, caused by step difference and
random error. As n increases, the size of the difference is expected to decrease.
If the measured maximum difference is smaller than expected, then the prob-
ability that the distributions are the same is high.
Note that the K-S criterion is very demanding as n becomes large because
the K-S criterion is scaled by the square root of n, reflecting an expected
decrease in the step-size error. The random error and outliers then dominate,
with outliers having a strong effect on the reported value for α (because K-S is
a measure of maximum deviation).
The Anderson-Darling statistic is a modification of the K-S test that gives
more weight to the data in the tails of the distribution. It requires a known
distribution for which critical values are calculated.

Goodness of Fit

Minitab

Use Stat\Basic Statistics\Normality Test.
Use the reported p value for the null hypothesis that the data follow the speci-
fied distribution. Values less than 0.05 generally indicate that the fitted distri-
bution is not a good match.
Excel

Using Green Belt XL Add-On
Use New Chart\Normal Probability Chart. (Note: The K-S value is also reported
on histograms and control charts where the histogram is displayed.)
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