Page 260 - Six Sigma Demystified

240 Six SigMa DemystifieD

confidence level, the hypothesis that the data have the same distribution
function as a proposed function. The Kolmogorov-Smirnov (K-S) goodness-
of-fit statistic should be used as a relative indicator of curve fit.

For example, the K-S goodness-of-fit test is 0.31 for the preceding order
fulfillment cycle time data, indicating a relatively poor fit for the normal distri-
bution. Figure F.9 shows the Quality America Green Belt XL software’s John-
son curve fit to the data. The predicted percentage exceeding the upper
specification limit for the Johnson distribution is 7.89 percent. Note that the
shape of the data differs significantly from the normal assumption, with a nega-
tive skew and bound at zero. The normal distribution would incorrectly esti-
mate that 6.7 percent of the process would be less than zero (i.e., z = –1.50),
which is quite impossible for the cycle time metric.

Johnson Distributions

Minitab

Use Stat\Quality Tools\Individual Distribution Identification to fit a Johnson dis-
tribution to the data. Use goodness-of-fit tests (described below) to determine
if an assumed distribution provides a reasonable approximation.

Excel

Using Green Belt XL Add-On

Use New Chart\Histogram. (Note: The histogram also may be displayed as an
option with the X and individual-X control charts.) Use goodness-of-fit tests
(described below) to determine whether an assumed distribution provides a
reasonable approximation.

equality-of-Variance Tests

Equality-of-variance tests indicate whether given subsets of data have compa-
rable levels of variation. Equal variance is a critical assumption in ANOVA.