Page 643 - Design for Six Sigma a Roadmap for Product Development

596 Chapter Sixteen

Larger-the-better requirement. For the “larger-the-better” requirement,
the quality loss function is
1
L(y) A 0 0
2
y 2
If the internal repair cost is A at producer tolerance , by letting repair
cost equal to quality loss, we obtain
1
2
A A 0 0
2
Therefore

A 0
0 0 (16.33)
A

Example 16.13. Strength of a Cable Suppose that a cable is used to hang
a piece of equipment, and that the equipment could produce a pull of 5000 kgf
(kilograms-force) to the cable. If the cable breaks and the equipment falls
off, the cost would be $300,000. The cable’s strength is proportional to the
2
cross-sectional area at 150 kgf/mm . Assume that the cost of cable is pro-
2
portional to its cross-sectional area at $60/mm .
Letting the area be x, then A 60x, and 150x, and using Eq. (16.33),
we obtain

300,000
150x 5000
60x

2
2
Then (150x) 60x 5000
300,000. We can solve for x: x 177. So the
cable cost A 60x $10,620 and cable strength D 150 150x 150
177 26,550. The safety factor

300,000
5.31
10,620

16.5.2 Determination of tolerance of low-level
characteristic from high-level tolerance
Given the transfer function of a high-level requirement y and low-level
characteristics x 1 ,x 2 ,…,x i ,…,x n , we have
y f(x 1 ,x 2 ,…,x i ,…,x n )

Taguchi tolerance design also has its own approach for determining
low-level tolerances. If the transfer function expressed above can be