Page 162 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

Char Count= 0
2:57
August 31, 2006
JWBK119-10
Monte Carlo Simulation 147
Histogram of NeqSquare
3-Parameter Lognormal
Loc −2.410
90 Scale 0.1301
Thresh 0.1340
80 N 1000
70
Frequency 50
60

40
30
20
10
0
0.20 0.21 0.22 0.23 0.24 0.25 0.26
NeqSquare

Summary for transform NegSquare
Anderson-Darling Normality Test
A-Squared 0.36
P-Value 0.445
Mean 19.987
StDev 2.072
Variance 4.295
Skewness 0.0767670
Kurtosis 0.0301912
N 1000
Minimum 13.913
1st Quartile 18.482
Median 20.012
14 16 18 20 22 24 26 3rd Quartile 21.373
Maximum 26.569
95% Confidence Interval for Mean
19.858 20.116
95% Confidence Interval for Median
95% Confidence Intervals 19.820 20.161
95% Confidence Interval for StDev
Mean 1.985 2.167
Median
19.8 19.9 20.0 20.1 20.2

Figure 10.16 Comparison of process capability between Box--Cox with power −2 and three-
parameter lognormal fit.

Data set 2 was generated using the three-parameter lognormal distribution with
location −2.5, scale 0.13, and threshold 0.1. The histogram with the best-fit distribution
and Box--Cox transformed (with λ =−2) distribution are shown in Figure 10.16. The
p-valuefromtheAnderson--Darlingnormalitytestis0.445,indicatingwecannotreject
the claim that the transformed distribution is normal and the Box--Cox transformation
is successful.