Page 154 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

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Illustration of the Two Methodologies Using a Case Study Data set 139
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D’Agostino and Stephens. If no exact p-value is found in the table, MINITAB calcu-
lates the p-value by interpolation.
Pearson correlation
The Pearson correlation measures the strength of the linear relationship between two
variables on a probability plot. If the distribution fits the data well, then the plot
points on a probability plot will fall on a straight line. The strength of the correlation
is measured by

z x z y
r =
N
where z x isthestandardnormalscoreforvariable Xand z y isthestandardnormalscore
for variable Y.If r =+1(−1) there is a perfect positive (negative) correlation between
the sample data and the specific distribution; r = 0 means there is no correlation.

Capability Estimation for our case study data using the best-fit distribution method
The graph in Figure 10.5 was plotted using MINITAB 14 with two goodness-of-fit
statistics, the Anderson--Darling statistic and Pearson correlation coefficient, to help
the user compare the fit of the distributions. From the probability plots, it looks like the
three-parameter loglogistic and three-parameter lognormal are equally good fits for
the data. From the statistics (Anderson--Darling and Pearson correlation), the three-
parameter loglogistic is marginally better.

Probability Plot for Data
LSXY Estimates-Complete Data
Correlation Coefficient
3-Parameter Weibull 3-Parameter Lognormal 3-Parameter Weibull
99 0.982
90 3-Parameter Lognormal
90 0.989
50 3-Parameter Loglogistic
Percent 10 Percent 50 2-Parameter Exponential
0.991
10
1 1
0.1 1.0 10.0 1 2 5
Data - Threshold Data - Threshold
3-Parameter Loglogistic 2-Parameter Exponential
99
90
90
50
Percent 50 Percent 10
10
1 1
1 10 0.001 0.010 0.100 1.000 10.000
Data - Threshold Data - Threshold
Goodness-of-Fit Anderson-Darling Correlation
(adj) Coefficient
Distribution 1.010 0.982
3-parameter Weibull 0.698 0.989
3-parameter Lognormal 0.637 0.991
3-parameter Loglogistic 3.071
2-parameter Exponential
Figure 10.5 Probability plots for identification of best-fit distribution.