Page 190 - Six Sigma for electronics design and manufacturing

The Use of Six Sigma with High- and Low-Volume Products and Processes
EV = R /d 2 = 0.025/1.128 = 0.02216
EV = 5.15· EV = 0.114; or alternately, EV = R · K 1 = 0.025·4.56 = 0.114
Example 5.14
The same process in Example 5.13 is to be analyzed for repeatability
and reproducibility with the addition of a second operator measuring
the same set of five parts:
A
B
Operator
________________ _______________ 159
Trial Trial
________________ _______________
Trial # 1 2 Range 1 2 Range
1 1.000 1.010 0.010 0.990 1.010 0.020
2 1.015 0.995 0.020 0.990 1.000 0.010
3 0.980 1.015 0.035 1.020 1.000 0.020
4 0.995 1.010 0.015 1.030 1.040 0.010
5 0.980 1.025 0.045 1.020 1.000 0.020
Total 4.970 5.055 0.125 5.050 5.050 0.080
X = 1.0025 R = 0.025 X = 1.010 R = 0.016
– –
R = 0.0205 X diff = 0.0075
– –
EV = R/d 2 = 0.01817
– –
EV= 5.15· EV = 0.094; or alternately, EV= R ·K 1 = 0.0205·4.56 = 0.094
2
AV = [( 0 .0 0 7 5 · 3 .6 5 ) – E V ] /n r = (0 .0 0 0 7 5 – 0 .0 9 4 ) /1 0 = – 0 = 0
2
2
In this case, the AV variation is smaller than the EV, so it is set to zero:
2
2
GR&R = EV + AV = EV = 0.94
5.3.3 GR&R results interpretation
GR&R represents 99% of the measurement error caused by either op-
erator or equipment. It is usually expressed as a percentage of the to-
tal variation (TV). The GR&R percentage = GR&R/TV, which is the
portion of the total variation consumed by the GR&R measurement
error, can be derived from the following sources:
1. The specification limits have historically been used as the total
variation, since it is assumed that the test of the product or part
will cull out any parts outside the specifications.
2. The total variation is comprised of RSS of the GR&R and the part
variation (PV). The part variation, P , which is also the population
variation used for six sigma calculations, can be derived from the