Page 213 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
180
Assuming actual deviations from the target value of a set of 18
PCBs at fabrication shop: 0, 0, –3, 0, 0, 1, 0, –5, –2, –2, 3, –5, –1, 0, –4,
3, 0, 1. Then
A
· MSD, MSD = (Y – M)
L =
2

1
2
MSD =
(Y 1 + Y 2 + Y 3 + . . . + Y n )
2
N
where n is the number of Y deviations. 2 2 2
1
MSD = (0 + 0 + . . . + 1.0 ) = 5.778 mm
2
2
2
18
A $500
L = · MSD = · 5.778 = $80.25/PCB
2 36
or
n = 2.274; average deviation from target = –0.778
A $500
2
2
2
L = [( – m) + ] = · (0.778 + 2.274 ) = $80.25/PCB
2
2 36
There are two ways to improve quality: set the average to target, or
reduce variability. It can be readily seen that the second alternative
results in the greatest quality cost improvement:
A $500
2
2
L Average = · = · (–0.778) = $8.40/PCB
2
36
A $500
2
2
L Variability = 2 · ( – m) = · (2.274) = $71.84/PCB
36
The importance of the loss function is that it gives a monetary value
to the state of the output of the process, both in terms of the process
average not meeting the specification nominal and the process devia-
tion. In the example outlined above, the average for all 18 measure-
ment was –0.78 mm and the standard deviation was 2.274. Note that
in this case the n , which is 2.274, is different than the n–1 , which is
2.34. The maximum loss function for an assembled PCB that causes
customer dissatisfaction is set at $500, and if it does not cause dissat-
isfaction, there is no loss. Using the formula, the loss due to the
process average not being equal to target is calculated to be $8.40,
whereas the loss due to variability around the average is $71.84.
Taguchi used this technique to compare two Sony television factories
in Tokyo and San Diego, CA in 1973.