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August 31, 2006
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JWBK119-10
146 Process Capability Analysis for Non-Normal Data with MINITAB
10.4.1 Simulated data sets
Data set 1 was generated using the three-parameter lognormal distribution with the
following parameters: location =−3.5; scale = 0.2; threshold = 0.1. The histogram
with the best-fit distribution and Box--Cox transformed (with λ =−3) distribution
are shown in Figure 10.15. The p-value from the Anderson--Darling normality test is
0.91, indicating we cannot reject the claim that the transformed distribution is normal
and the Box--Cox transformation is successful.

Histogram of NegThird
3-Parameter Lognormal
120 Loc −3.533
Scale 0.2016
Thresh 0.09457
100 N 1000

80
Frequency 60

40

20

0
0.114 0.120 0.126 0.132 0.138 0.144 0.150
NegThird

Summary for transform NegThird
Anderson-Darling Normality Test
A-Squared 0.18
P-Value 0.910
Mean 526.62
StDev 74.23
Variance 5509.84
Skewness −0.029462
Kurtosis −0.100286
N 1000
Minimum 283.51
1st Quartile 475.79
Median 528.07
320 400 480 560 640 720 3rd Quartile 576.98
Maximum 763.87
95% Confidence Interval for Mean
522.02 531.23
95% Confidence Interval for Median
95 % Confidence Intervals 522.20 533.84
95% Confidence Interval for StDev
Mean 71.11 77.63
Median
522 524 526 528 530 532 534

Figure 10.15 Comparison of process capability between Box--Cox with power −3 and lognor-
mal fit.