Page 633 - Design for Six Sigma a Roadmap for Product Development

586 Chapter Sixteen

Use this equation to calculate current C p for the high-level require-
ment; if this C p meets the requirement, stop. If not, go to step 5.
Step 5. Select a desirable C p level. For example, if Six Sigma level
is required, then C p 2.
Compute the required high-level variance by

0 2
2
req
3C p
In order to achieve this high-level variance requirement, we need to
“scale down” low-level variances. If proportional scaling is used, we
can use the following formula to find the scaling factor p:

n ∂f 2

req p 2
2 i (16.17)
2
i 1 ∂x i
So
req
p (16.18)
x i 2 i
n

∂ f

2

∂
i 1
Then the lower-level variance and tolerance can be determined by
(16.19)
i new p i
(16.20)
i 3C p i new
Example 16.9. RL Circuits Revisited Recall that in Example 16.6, a 100-V,
f-Hz power supply across a resistance R in series with an inductance L will
result in a current of y amperes:
100
y
R (2 fL ) 2
2
Assuming that f 50 Hz, the nominal value for the resistor T R 9.5 , the
current tolerance R 1.0 , the nominal value for the inductor T L 0.01
H, and the current tolerance L 0.006 H. Assume that for both R and L,
C p 1.33.
The customer’s tolerance for the circuit current is y 10.0 1.0 A, and
we would like to satisfy this requirement with C p 2.0. So the required
standard deviation for the current y is
1.0
0
req 0.1667
3C p 3
2.0