Process capability index: A better way to assess equipment capability
Figure 1. Schematic of the test stencil.
Figure 4. Process capability of Printer 2.
Figure 2. Y offset distribution plot for Printer 1.
Figure 3. Y offset distribution plot for Printer 2. Figure 5. Process capability of Printer 1.
even though both printers have the
Printer 1: 0.72 ≤ Cpk ≤ 0.91 • A good process engineer should
same stated accuracy, they clearly do not
Printer 2: 2.10 ≤ Cpk ≤ 2.59 know how to calculate process
perform similarly. It should be of inter-
capability indices (Cp, Cpk and oth-
Even when a confidence interval is
est to note that there are even examples
ers), but before doing so must as-
generated for each printer, Printer 1 is
in which a printer with a better stated
sure that the process is in statistical
still inferior and incapable because the CI
accuracy (e.g., + 10 µ) can be shown to be
control and the data are normally
does not contain 1.0 (or a better hurdle
inferior to that of one with a poorer stated
distributed,
of, say, 1.33). The reader should notice
accuracy (e.g., + 25 µ) when the application
• A good process engineer should
that it does have a good Cp estimate (1.33).
(specification range) is considered.
understand how a process capabil-
However, because it is off-center (Y offset
Returning to the above example, the
ity index value relates to defect
target = 0.000 mm and it has a sample
sample standard deviations are such that
levels,
mean approximately equal to 0.010 mm),
the capability of each printer (before com-
• A good process engineer should
this adversely affects the actual process
paring to the specifications of the offset)
realize that population param-
capability (Cpk). When the CI is considered
concur with the stated accuracy of + 25 µ.
eters rarely, if ever, are used and
for Printer 2, its lower confidence limit
However, Printer 2 clearly has a superior
therefore the resulting calculations
is still above 2.00, indicating it to be an
centering and lower variability than Printer
are most likely based upon samples
exceptional print process.
1. The estimate of Cpk for Printer 2 (2.34) is
from a process, thus yielding esti-
much better than that of Printer 1 (0.82).
summary
mated values of Cp, Cpk, etc.,
Following the earlier suggestion, the 95%
• A good process engineer should
In summary, we would like to stress the
confidence intervals for each printer’s Cpk
realize that one process can yield
following points:
appear below.
Continued on page 50
24 – Global SMT & Packaging – September 2008
www.globalsmt.net
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