Page 192 - Six Sigma for electronics design and manufacturing

The Use of Six Sigma with High- and Low-Volume Products and Processes
GR&R% from specifications. If the specifications are given as ±0.500,
then GR&R% = 0.2351/0.500 = 47%.
GR&R% from part variation. Taking the range of part averages from
the data:
R p = 1.0167 – 0.4583 = 0.55833
PV = R p · K 3(n=10) = 0.55833 · 1.62 = 0.9045
2
2
2
2
TV = G R & R + T V = 0 .2 3 5 1 + 0 .9 0 4 5 = 0.9346
GR&R% = 100(GR&R/TV) = 0.2351/0.9346 = 25% 161
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 GR&R 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 2(n=3) = 2/1.693 = 1.18133
s EV = / n = 1.18133/1.732 = 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 = ±SL/3 = 3/(3 · 1.18133) = 0.85
Cpk = min (8 – 5.11)/(3 · 1.18133) = 0.82 or 3.11/(3 · 1.18133)
= 0.82