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Chapter 13: G. Measurement System Analysis 125
2 2 2
s = s + s
(13.2)
Total Parts Gage
2 2 2
s = s + s + s
2
. . ×
Gage Inst Operator Part Operator
(13.3)
The total variability due to the measurement system (s 2 Meas. or s 2 Gage) is also
known as the total GR&R variability. The instrument variability is represented
by the variability in the repeated measurements by the same operator and for this
reason it is also known as repeatability. In the ANOVA method, the repeatability
variance component is the error variance (that is s 2 inst = s 2 EV = s 2 ). The remainder
of the variability in the measurement system comes from the various operators
who use the instrument, and the interaction between the instruments and
the operators. Note that the interaction appears when any operator can measure
one type of part better than another. This total variability from the operators and
the interaction between the operators and the instruments is also known as reproducibility.
Thus, the equation (13.3) can also be expressed as
Part II.G
2 2 2
s = s + s . (13.4)
Gage Repeatability Reproducibility
Using Barrentine’s approach, repeatability is defined as
R
Repeatability = EV = 515 . ˆ = 515 .
d
s Repeatability
2
515 .
= KR where K = , (13.5)
1 1
d
2
and where the factor 5.15 represents the 99 percent range of the standard normal
distribution, which follows from the fact that
P( 2. 575 Z 2. 575)=
0. 99. (13.6)
60
Linearity
Observed value
50
40
30
20
20
25 30 35
Actual value
40 45 50 55
Figure 13.3
Diagram showing the linear relationship between the actual and the
observed values.