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Chapter 13: G. Measurement System Analysis 131
repeatability and the rest (0.56 percent) is contributed by the reproducibility. The
variation due to parts is 95.88 percent of the total variation. This implies that
the measurement system is very capable.
Note that the percent contributions are calculated simply by dividing the variance
components by the total variation and then multiplying by 100. Thus, the
percent contribution due to repeatability, for example, is given by
2.
7889
× 100 = 3. 55%.
78.
5243
The part of the Minitab printout shown in Figure 13.7 provides various percent
contributions using estimates of standard deviations, which are obtained by taking
the square root of the variance components. The comparison with standard
deviation does make more sense because the standard deviation uses the same
units as those of the measurements. The study variation (that is, measurement
system variation, which is equivalent to the process variation in the study of process
control) is obtained by multiplying the standard deviation by 6. The percent
study variations are calculated by dividing the standard deviation by the total
variation and then multiplying by 100. Thus, the percent contribution due to partto-part
variation, for example, is given by
Part II.G
10.
7868
× 100 = 17. 98%.
60
The percent tolerance is obtained by dividing the (6*SD) by the process tolerance
and then multiplying by 100. Thus, the process tolerance of total GR&R, for
example, is given by
10.
7868
× 100 = 17. 98%.
60
Note that the total percent tolerances in this example do not sum to 100. Rather,
the total sum is 88.61, which means the total variation is using 88.61 percent of the
specification band.
Study Var %Study Var %Tolerance
Source StdDev (SD) (6 * SD) (%SV) (SV/Toler)
Total Gage R&R 1.79780 10.7868 20.29 17.98
Repeatability 1.67000 10.0200 18.85 16.70
Reproducibility 0.66574 3.9944 7.51 6.66
Operators 0.00000 0.0000 0.00 0.00
Operators*Part Numbers 0.66574 3.9944 7.51 6.66
Part-To-Part 8.67711 52.0626 97.92 86.77
Total Variation 8.86139 53.1684 100.00 88.61
Number of Distinct Categories = 6
Figure 13.7 An example of Minitab printout.