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Table B.2 Contribution of each error source on force measurement system’s variation.
Source
Total Gage R&R
Repeatability
Reproducibility
Operators
Force platform
Parts*Operators
Parts*Force platform
Part-To-Part
Parts
Total Variation
Std. Dev (SD)
Study Var (6 × SD)
%Study Var (%SV)
%Tolerance (SV/Toler)
2,169
0,410
2,130
0,000
1,769
0,101
1,182
124,970
124,970
124,989
13,015
2,460
12,780
0,000
10,613
0,605
7,095
749,820
749,820
749,933
1,74
0,33
1,70
0,00
1,42
0,08
0,95
99,98
99,98
100,00
4,43
0,84
4,35
0,00
3,61
0,21
2,41
255,04
255,04
255,08
design of the gage experiment allowed to compare the measurement capability of the two force
platforms.
B.2.3.
Procedure
A calibrated load was placed by the operator at the geometrical center of the top plate of the force
platforms and the Fz of the GRF was recorded for 5 sec at sampling rate of 30 Hz. This process was
repeated for the 16 treatment combinations and their replications. The mean value and standard
deviation was computed for each sample. The force measurement system was zeroed before each
measurement.
The force measurement system uses a 12-bit precision A/D converter (resolution of
100
212
≈ 0.024%).
The Fz range during the measurements was set at 0 - 1250 N. Therefore, the Fz can be resolved
to
1250 N
212
= 0.31 N. As a guideline, the resolution should not be greater than 5% of the process
tolerance limits. Hence, the tolerance intervals of the measurement process should not be less
than 6.4 N. Manufacturer specified the maximum force error at e = 2% of the applied force, which
corresponds to e1 = 1.96 N, e2 = 3.92 N, e3 = 5.88 N, and e4 = 7.84 N. The conformance zone
is the tolerance interval reduced by the measuring uncertainty at each end. Therefore, if the
uncertainty is the 30% of the tolerance and the rest 70% is the conformance zone, the tolerance
intervals for each load and for the corresponding errors are T1 = 6.53 N, T2 = 13.07 N, T3 = 19.6
N, and T4 = 26.13 N.
B.2.4.
Statistics
Prior to model analysis, the Grubbs’ test was used to check for outliers. A three-factor random-effect
linear model with 2-order interactions was fitted to the data to analyze the factorial design experiment and hence to quantify the R&R variance component. To compare measurement capability
between force platforms, a two-factor random-effect linear model with 2-order interactions was
fitted to the data for every part seperately and the R&R variance components were compared. It
was supposed that reproducibility is less than repeatability, indicating that most of the variability
is accounted for by the inaccuracy of the measurement system and not by operators’ variability
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