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August 31, 2006
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JWBK119-10
148 Process Capability Analysis for Non-Normal Data with MINITAB

Histogram of Neg1
3-Parameter Lognormal
120 Loc −2.181
Scale 0.3493
Thresh 0.1213
100 N 1000
80
Frequency 60

40

20

0
0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44
Neg1

Summary for transform Neg1
Anderson-Darling Normality Test
A-Squared 0.32
P-Value 0.541
Mean 4.2656
StDev 0.6995
Variance 0.4894
Skewness −0.024580
Kurtosis −0.287026
N 1000
Minimum 2.2671
1st Quartile 3.7875
Median 4.2675
2.4 3.0 3.6 4.2 4.8 5.4 6.0 3rd Quartile 4.7514
Maximum 6.3178
95% Confidence Interval for Mean
4.2222 4.3090
95% Confidence Interval for Median
95% Confidence Intervals 4.2156 4.3192
95% Confidence Interval for StDev
Mean 0.6702 0.7316
Median
4.22 4.24 4.26 4.28 4.30 4.32
Figure 10.17 Comparison of process capability between Box--Cox with power −1 and lognor-
mal fit.

Data set 3 was generated using the three-parameter lognormal distribution with
location −2, scale 0.3, and threshold 0.1. The histogram with the best-fit distribution
and Box--Cox transformed (with λ =−1) distribution are shown in Figure 10.17. The
p-valuefromtheAnderson--Darlingnormalitytestis0.541,indicatingwecannotreject
the claim that the transformed distribution is normal and the Box--Cox transformation
is successful.