Chemistry Reference
In-Depth Information
measured values and the “true values.” R&R is a combination of repeatability (E.V.)
and reproducibility (A.V.)
q
ðE
2
2
R&R ¼
:
V
:Þ
þðA
:
V
:Þ
ð9
:
113Þ
Part variation (P.V.) is the variation of the average of the measurements made for
different parts or samples. This variation is caused by the differences of the “true
values” between different parts. P.V. does not represent the accuracy of the measure-
ment system, but it does contribute to measurement variation.
q
ðR
p
K
p
Þ
2
2
P
:
V
: ¼
ðE
:
V
:Þ
=
t
:
ð9
:
114Þ
where R
p
¼ðR
A2
þR
B2
þR
C2
Þ=
3, and R
A2
, R
B2
, and R
C2
are ranges of part averages
for each operator. K
p
¼ 1
66 for 10 parts with 3 trials.
Total variation (T.V.) is the total measurement variation due to the measurement
system error and the part (sample) variation. T.V. is a combination of R&R. and P.V.
:
q
ðE
2
2
2
T
:
V
: ¼
:
V
:Þ
þðA
:
V
:Þ
þðP
:
V
:Þ
ð9
:
115Þ
All the stress measurement results and gage R&R test results are listed in Table 9.9.
Since the sign of the stress has no effect on the gage R&R test, all stress values referred
to are in absolute values without negative signs. The results show that the measure-
ment systemerror (R&R) is 37.6MPa, which is 6 percent of the average residual stress
value (627.8MPa) for all 90 measurements. The two components of the R&R value
are repeatability (E.V.) ¼34.7MPa and reproducibility (A.V.) ¼14.5MPa. The total
variation (T.V.) is large (177.9MPa); however, the majority of it comes from the
part variation (P.V.). Taking the total measurement variation (T.V.) as 100 percent,
the part variation (P.V.) is 97.7 percent, and the measurement system error (R&R) is
21.1 percent. It must be noted that all component variations do not simply add up to
100 percent due to the square root relation.
APPENDIX 9.A CALCULATION OF PRINCIPAL STRESSES FROM
THE GENERAL STRESS TENSOR
Appendix 9.A.1 Calculate Principal Stresses
The principal stress components, s
I
, s
II
, and s
III
, also called eigenvalues, can be
calculated from the tensor:
2
4
3
5
s
11
s
12
s
13
s
12
s
22
s
23
s
13
s
23
s
33
