Page 212 - Six Sigma for electronics design and manufacturing

Six Sigma Quality and Manufacturing Costs of Electronics Products
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characteristic average versus its target value and the distribution
around the average. Generally, it is expressed in terms of the cost of
each failure divided by the square of the deviation from the average at
which the failure occurs:
A
L(y) =
where
L = loss function
y = design characteristic 2 (y – m) 2 (6.1)
m = target value or specification nominal
A = cost of repair or replacement of the product
= functional limit of the product, where customer dissatisfaction oc-
curs. This could be wider than the product specifications.
2
Rewriting the formula by using the fact that (y – m) is similar to
the expression for mean square deviation (MSD) or the variance for
the product characteristics:
A
L = · MSD (6.2)
2
The loss formula can be translated into familiar statistical terms of
actual product characteristic average and the standard deviation .
The term is based on the n divisor of the standard deviation formula
and not n – 1 for the sample deviation:
A
L = [( – m) + ] (6.3)
2
2
2
6.2.2 Quality loss function example
An example of the quality problems that occur in the fabrication of
printed circuit boards (PCBs) is the fit of a PCB edge male connector
into the product housing female connector or “card cage.” If the vari-
ability of the edge connector size is large, the fit is difficult or impossi-
ble to achieve, which could result in scrapping the PCB.
Assume that the tolerance for acceptable fit is ±6 mm, the cost of re-
moving a defect in the PCB at the fabrication shop is $100, and the
cost of removing a defect at the customer site after the PCB has been
assembled is $500. A typical lot of 18 PCBs from the PCB fabricator
was measured. The following shows the calculations of the loss func-
tion due to the variability of the edge connector and estimation of the
savings incurred by either adjusting the average to target or reducing
variability of the PCB edge connector.