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Statistical Process Control (SPC) (Page 5 of 5)
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The
quantity
(USL - LSL)
is basically the range of output that the process must
meet,
while 6 sigma corresponds to
+/- 3 sigma
from the mean, or
99.73%
of all the process output
data. The smaller the value of 6 sigma, the narrower the
process output distribution is, denoting higher stability. Thus,
Cp increases as process
stability increases.
Thus, a process needs a
Cp > 1
to ensure that it is
narrow enough
to meet the spec range 99.73% of the time.
Although Cp
indicates the stability of a process, it has one major drawback that
makes it almost useless in the semiconductor industry. It does
not
consider the
centering
of the process distribution within the spec limits. A process with
a Cp of 100 may be very stable, with all its output data very close to
each other, but it may also be out-of-spec at all times, i.e., if it is
centered outside the spec limits!
This weakness
of Cp is addressed by another process capability index, Cpk.
Cpk measures how centered the output of the process is
between its lower and upper limits, as well as how variable the output is. Cpk
is expressed as the
ratio
of how far the
mean
of the output data is from the closer spec limit (the centering of the
process) to three times their
standard deviation
(the process variability).
What these
formulae mean is this: Cpk is equal to whichever is
lower
between
An
ideal process is one whose output is always dead center between the spec
limits, such that the mean of its output data equals this dead center
and the standard deviation is zero. The
Cpk of this ideal process
is infinite (so is the Cpk of other processes whose sigma = 0, as long
as the LSL<mean<USL).
The
Cpk decreases if one or both of the following occurs:
1) the data become less centered; and 2) the data become
more variable
(sigma increases). Thus,
improving the process capability of a process entails one or both of: 1)
centering the output between limits and 2) decreasing the variation of
the output data.
The
essence
of SPC,
therefore, is being able to
recognize whether a low Cpk is
due to the mean
of the process or its sigma,
and taking the necessary actions to correct the problem, be it centering
of the data or making them less variable. In any process, the
actions needed to center the output data may be
different
from what needs to be done to make the data less variable.
Knowledge
of this basic SPC principle is therefore a necessary weapon in every
process engineer's arsenal.
As of this
writing, most semiconductor companies
target
a Cpk of
1.67
for
their processes, although they would be satisfied to
have
an actual Cpk of at least
1.33.
Everything, of course, depends on what spec limits the customer imposes
on the manufacturer. Still, at the end of the day it should always
be the manufacturer's goal to
center
their output between these spec limits as
consistently
as possible.
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See Also:
Control Charting;
Cpk Vs. ppm Table;
Monitors & Controls;
Quality Systems
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