GRR results interpretation Determining Gauge Capability

GRR data by multiplying the range of part averages as measured by the operators by the constant K
3
. K
3
is calculated from d
2
in Table 5.6, depending on the number of parts examined in the
GRR measurements, as follows: PV = R
p
· K
3
5.16 K
3
= 5.15d
2
5.17 The values for K
3
are for number of parts examined in the GRR: K
3
= 3.65 2.70 2.30 2.08 1.93 1.82 1.74 1.67 1.62 n
p
= 2 3
4 5
6 7
8 9
10 TV =
G R
R
2
+ P V
2
5.18 3. If the process variation is known through process capability stud-
ies and is based on six sigma, then
P
can be derived independent- ly from the GRR study and used for PV and TV calculations, with
PV = 5.15 ·
P
. The GRR of total variation can be used to determine if the meas-
urement system is acceptable for its intended applications. General guidelines for the value of GRR are:
앫 If GRR 10, then the measurement system is acceptable 앫 If 10 GRR 30, then the system may be acceptable, based
on whether the part characteristic classification is not critical or from customer input
앫 If GRR0 30, then the system is not acceptable. It is then de- sirable to seek resolution through the use of quality tools, better
operator training, or the purchase of new inspection equipment.

5.3.4 GRR examples

Example 5.15 Table 5.7 is a complete GRR example of three operators and two tri-
als, measuring parts with specifications ±0.500. –
– R is obtained from
the average R of the three operators and is equal to 0.0383. X
diff
is ob- tained from the difference between the highest average operator and
the lowest and is equal to 0.0600. EV = X
X
d i
f f
· K
1
= 0.03833 · 4.56 = 0.1748 AV =
[ 0.0
6 · 2 .7
2
– E
V
2
nr ] = [0
.0 26244 –
0.1 748
2
20] = 0.1572
GRR = 0.1
748
2
+ 0 .1
572
2
= 0.2351
GRR from specifications. If the specifications are given as ±0.500, then GRR = 0.23510.500 = 47.
GRR from part variation. Taking the range of part averages from the data:
R
p
= 1.0167 – 0.4583 = 0.55833 PV = R
p
· K
3n=10
= 0.55833 · 1.62 = 0.9045 TV =
G R
R
2
+ T V
2
= 0.2 351
2
+ 0 .9
045
2
= 0.9346 GRR = 100GRRTV = 0.23510.9346 = 25
In this example, the measurement system is of marginal accept- ance.
Example 5.16 An analysis of a test system with a specifications limit of 5 ± 3 con-
sists of repeating a sample measurement three times by three opera- tors:
Operator Measurements
R X
1 4
6 4
2 4.67
2 4
5 6
2 5.00
3 5
5 7
2 5.67
X
d i
f f
= 1 Average
2 5.11
Show quality control, six sigma, and GRR analysis. For the control chart:
R = 2, n = 3; UCL
R
= R · D
4
= 2 · 2.57 = 5.14; LCL
R
= 0
EV
= R d
2n=3
= 21.693 = 1.18133 s
EV
= n
= 1.181331.732 = 0.68; 3s = 2.04 –
– X = chart centerline = 5.11
UCL
x
= 5.11 + A
2
· R = 7.15; or UCL
x
= 5.11 + 3s = 7.15 LCL
x
= 5.11 – 2.04 = 3.07 For six sigma calculations:
Average shift = 0.1111 Cp = ±SL3
= 33 · 1.18133 = 0.85 Cpk = min 8 – 5.113 · 1.18133 = 0.82 or 3.113 · 1.18133
= 0.82