Page 158 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

August 31, 2006
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JWBK119-10
A Further Case Study 143
Box-Cox Plot of Case Study #2
Lower CL Upper CL
5.0 Lambda
(using 95.0% confidence)
Estimate −1.70551
4.5 Lower CL −2.84817
Upper CL −0.52515
Best Value −2.00000
4.0
StDev 3.5

3.0

2.5 Limit
−5.0 −2.5 0.0 2.5 5.0
Lambda
Figure 10.10 Box--Cox plot of Case Study 2.

10.3.2 Process capability analysis using the best-fit distribution
From the probability plot and the Anderson--Darling statistics in Figure 10.13, the
best-fit distribution for the data is the three-parameter lognormal distribution.
Using the three-parameter lognormal distribution to fit the data, with USL = 75, we
obtained the histogram plot with the fitted distribution and the estimated C pk shown

Summary for Transform
Anderson-Darling Normality Test
A-Squared 0.13
P-Value 0.982
Mean 0.002797
StDev 0.000698
Variance 0.000000
Skewness 0.075943
Kurtosis −0.281335
N 100
Minimum 0.001125
1st Quartile 0.002291
Median 0.002813
0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 0.0045 3rd Quartile 0.003272
Maximum 0.004553
95% Confidence Interval for Mean
0.002658 0.002935
95% Confidence Interval for Median
0.002542 0.002991
95% Confidence Intervals
95% Confidence Interval for StDev
Mean 0.000613 0.000811
Median
0.0025 0.0026 0.0027 0.0028 0.0029 0.0030
Figure 10.11 Summary statistics and histogram of the transformed data of Case Study 2.