Page 74 - Six Sigma for electronics design and manufacturing

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The Elements of Six Sigma and Their Determination
interaction of the specifications versus the manufacturing distribu-
tion. A capability constant k is provided to calculate Cpk:
process shift
k =
and
Cpk = Cp (1 – k)
(USL – LSL)/2
A more direct method for calculating Cpk is to divide the two halves
of the distribution as to their interaction with the specification limits:
USL – process average
(2.4)
3
Cpk = min (2.5)
process average – LSL

3
When the average shift of the process from specification nominal is
equal to zero, then the Cp and Cpk terms are equal.
SL
Cpk = Cp = ± , when process average shift from nominal = 0 (2.6)
3
where
Cp is the process capability index
k is the Cpk constant
USL and LSL are the upper and lower design specifications limits in
units of geometry (mm) or output (volts)
SL is the specification limit interval equal to USL or LSL minus the
nominal
is the standard deviation of the manufacturing process
In the design community, Cp = 1 is also called 3 design, and Cp =
1.33 is called 4 design.
2.2.1 Cpk and process average shift
When there is a manufacturing process average shift, the value of
Cpk is not equal to the value of Cp. Using Equation 2.5, Cpk can be
calculated for a multitude of conditions, as shown in Figure 2.7. The
figure shows specification limits of 27 ± 6, and a varying set of
processes, with average and standard given for each. It can clear-
ly be shown that when the average is equal to the specification nomi-
nal, then Cp = Cpk. When the average is shifted, either left or right,
then the Cpk value is always less than the Cp.
When this process is reversed—with Cpk given with no information
about the process—the amount of average shift with respect to specifi-
cation nominal cannot be calculated. Table 2.2 is a good illustration of