Drawing charts and graphs with process data
helps the audience to visualize the behavior
of the process. Visual representations may be
insufficient to make decisions about whether
the process generating the data is performing
in a way that meets various requirements. Control
charts, for example, provide information about
whether the process is in control. These charts
calculate the mean and standard deviation for
the plotted data points. This information summarizes
how the process is actually performing. Even
if the process is in control, it may not be
producing parts that meet specification limits.
Typically, the specification limits are requirements
set by the customer. In order to produce viable
products, a process must be in control in order
to produce a consistent product and the process
must be capable of meeting customer specifications.
There are several indices that can be calculated
to aid in the determination of the process capability.
These can be calculated using the Statit gpc
command or QC>Variable Charts>Process
Capability Chart from the menu. The statistics
calculated in this analysis describe the process
from different aspects. The Cp, Cr and Cpk indices
evaluate the short term variation in the process
or the inherent process variation. These indicators
look at the variation within subgroups. In contrast,
Pp and Ppk evaluate the long term variation
or the process performance by using the variation
from all the data. The calculations for the
Cp, Pp and Cr indices exclude the effect of
the actual process mean. The subtle differences
between these indices help to improve the clarity
of process capability.
In addition to those mentioned already, there
is another index that can be calculated that
is more sensitive to the process deviation between
the mean and the target. This is the Cpm index.
This index attempts to characterize the proximity
of the process mean to the target value, T.
Since this difference is factored in the calculation,
deviations from target cause the denominator
to increase. The increase, therefore, causes
the Cpm value to become smaller.
Cpm is calculated using the following formula:
| Cpm = |
 |
In the denominator, the term that calculates
the difference between the process mean and
the target value is squared. This term actually
penalizes the process when the mean deviates
from the target. The farther the process mean
moves away from the target, the larger the penalty
becomes. The formula also illustrates that if
the mean and target are equal, then the results
of the Cpm equation will equal Cp.
Here is an example of the Process Capability
Chart in Statit Custom QC.
We can add the Cpm index to this chart with
the following statements:
#cpmU
= (#usl-#mean)/(3*sqrt(#sigma**2 +(#mean-#csl)**2))
#cpmL = (#mean-#lsl)/(3*sqrt(#sigma**2 +(#mean-#csl)**2))
#cpmk = minof(#cpmU,#cpmL)
%cpmlab = "Cpm Index: "
text 1 %cpmlab /location=652 /anchor=LC 126
%cpm = "=" // putwith((#usl-#lsl)/(6*sqrt(#sigma**2
+(#mean--#csl)**2)),"%6.3f")
text 2 %cpm /location=893 126 /anchor=LC
text 3 "Cpmk:" /location=625 100 /anchor
= LC
%cpmk = "=" & putwith(#cpmk,"%-6.3f")
text 4 %cpmk /location=875 100 /anchor = LC
The position of the Cpm label and value can
be modified at user’s discretion.
In conclusion, it should be noted that process
capability should only be performed on a stable
process. If the process is not in control, the
capability results may be erroneous. The indices
are also sensitive to the distribution. If the
data are not normally distributed, the process
capability indices may not provide adequate
inference about the observed capability.
See also Discussions
on Normality.
