Page 189 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
158
d*
n/m
d 2
2
1.128
1.410
3
1.906
1.693
2.237
2.059
4
2.326
5
2.477
2.669
6
2.534
2.704
7
2.827
2.847
2.961
8
2.970
9
3.076
3.078
3.178
10 Table 5.6 R estimator of for GR&R 2
d 2 = unbiased R estimator for (n = sample subgroup size).
d* = biased R estimator based on m = number of trials.
2
= R /d 2 .
= X d i f f difference (highest to lowest trial averages)/d* . 2
or

2
EV
2
AV = (X d i f f · K 2 ) – (5.15)
nr
where AV is related directly to X d i f f by the factor K 2 . K 2 is equal to
3.65 for r = 2 and 2.70 for r = 3. This is derived from the relation-
ship K 2 = 5.15/d * or 5.15/1.410 = 3.65 for r = 2 and 5.15/1.906 =
2
3.05 for r = 3. If the result of subtraction in the AV terms inside the
square root term is negative, then AV should be set to zero.
7. The GR&R is calculated from the RSS of EV and AV. In most cases,
it is expressed as a percentage of the total specification span.
5.3.2 Examples of GR&R calculations
Example 5.13
A process is to be analyzed for repeatability using one operator (A)
measuring five parts, two times each, on one machine. The data is
arranged as follows:
Operator A Trial
Trial # 1 2 Range
1 1.000 1.010 0.010
2 1.015 0.995 0.020
3 0.980 1.015 0.035
4 0.995 1.010 0.015
5 0.980 1.025 0.045
Total 4.970 5.055 0.125
X = 1.0025 R = 0.025