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132 Part II: Metrology
The last entry in the Minitab printout is the number of distinct categories,
which in this case is six. The number of distinct categories can be determined as
shown below:
part-to-part SD
Number of distinct categories = Integral part of
Total gage R&R SD × 1414 . 2
8.
67711
= Integral part of ×
1.
79780 1
.4142 6
= .
Part II.G
Under AIAG’s recommendations, a measurement system is capable if the number
of categories is greater than or equal to five. Thus, in this example, the measurement
system is capable of separating the parts into the different categories that
they belong to. This quantity is equivalent to the one defined in AIAG (2002) and
Montgomery (2005) and is referred to as signal-to-noise ratio (SNR), that is,
SNR =
2r
p
1 r
p
(13.10)
where
r
p
2
s
p
= . (13.11)
2
s
Total
Graphical Representation of Gage R&R Study
Figure 13.8 shows the various percent contributions of gage R&R, repeatability,
reproducibility, and part-to part variations discussed in the above paragraph.
In Figure 13.9, we first interpret the R chart. All the data points are within
the control limits, which indicates that the operators are measuring consistently.
However, the X – chart shows many points beyond the control limits. But this does
not mean the measurement system is out of control. Rather, this indicates narrower
control limits because the variation due to repeatability is small and the measurement
system is capable of distinguishing the different parts.
Figure 13.10 plots the average of each part by any single operator. In this example,
we have three line graphs since we had three operators. These line graphs
intersect each other but are also very close to each other. This implies that there
is some interaction between the operators and parts. Thus, for instance, in this
example there is some interaction, which is significant only at 0.131 or greater level
of significance.
In Figure 13.11 the clear circles represent the measurements by each operator
and the black circles represent the means. The spread of measurements for
each operator is almost the same. The means fall on a horizontal line, which indicates
that the average measurement for each operator is also about the same. Thus,
in this example the operators are measuring the parts consistently. In other words,
the variation due to reproducibility is low.