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Interpreting
Process Capability
Part three of a three
part series.
The following is
an excerpt from The
Quality Engineering Handbook by Thomas
Pyzdek, © Quality Publishing. It may be ordered from the Quality
Publishing Order Form.
Perhaps the biggest drawback
of using process capability indexes is that they take the analysis a step
away from the data. The danger is that the analyst will lose sight of
the purpose of the capability analysis, which is to improve quality. To
the extent that capability indexes help accomplish this goal, they are
worthwhile. To the extent that they distract from the goal, they are harmful.
The quality engineer should continually refer to this principle when interpreting
capability indexes.
CP
Historically, this is one of the first capability indexes used. The "natural
tolerance" of the process is computed as 6s . The index simply makes
a direct comparison of the process natural tolerance to the engineering
requirements. Assuming the process distribution is normal and the process
average is exactly centered between the engineering requirements, a CP
index of 1 would give a "capable process." However, to allow
a bit of room for process drift, the generally accepted minimum value
for CP is 1.33. In general, the larger CP is, the
better. The CP index has two major shortcomings. First, it
can’t be used unless there are both upper and lower specifications.
Second, it does not account for process centering. If the process average
is not exactly centered relative to the engineering requirements, the
CP index will give misleading results. In recent years, the
CP index has largely been replaced by CPK (see below).
CR
The CR index is algebraically equivalent to the CP
index. The index simply makes a direct comparison of the process to the
engineering requirements. Assuming the process distribution is normal
and the process average is exactly centered between the engineering requirements,
a CR index of 100% would give a "capable process."
However, to allow a bit of room for process drift, the generally accepted
maximum value for CR is 75%. In general, the smaller CR
is, the better. The CR index suffers from the same shortcomings
as the CP index.
CM
The CM index is generally used to evaluate machine capability
studies, rather than full-blown process capability studies. Since variation
will increase when normal sources of process variation are added (e.g.,
tooling, fixtures, materials, etc.), CM uses a four sigma spread
rather than a three sigma spread.
ZU
The ZU index measures the process location (central tendency)
relative to its standard deviation and the upper requirement. If the distribution
is normal, the value of ZU can be used to determine the percentage
above the upper requirement by using Table 4 in the appendix of The
Complete Guide to the CQM. The method is the same as described
in Chapter III.B using the Z statistic, simply use ZU instead
of using Z. In general, the bigger ZU is, the better. A value
of at least +3 is required to assure that 0.1% or less defective will
be produced. A value of +4 is generally desired to allow some room for
process drift.
ZL
The ZL index measures the process location relative to its
standard deviation and the lower requirement. If the distribution is normal,
the value of ZL can be used to determine the percentage above
the upper requirement by using Table 4 in the appendix of The Complete
Guide to the CQM. The method is the same as described in III.B
[of The Complete Guide to the CQM] using the Z transformation,
except that you use -ZL instead of using Z. In general, the
bigger ZL is, the better. A value of at least +3 is required
to assure that 0.1% or less defective will be produced. A value of +4
is generally desired to allow some room for process drift.
ZMIN
The value of ZMIN is simply the smaller of the ZL
or the ZU values. It is used in computing CPK.
CPK
The value of CPK is simply ZMIN divided by 3. Since
the smallest value represents the nearest specification, the value of
CPK tells you if the process is truly capable of meeting requirements.
A CPK of at least +1 is required, and +1.33 is preferred. Note
that CPK is closely related to CP, and that the
difference between CPK and CP represents the potential
gain to be had from centering the process.
CPM
A CPM of at least 1 is required, and 1.33 is preferred. CPM
is closely related to CP. The difference represents the potential
gain to be obtained by moving the process mean closer to the target. Unlike
CPK, the target need not be the center of the specification
range.
Follow these links to
read Parts One and Two of the Process Capability Series:
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