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Interpreting a Process Capability Chart
Since process capability
is not valid unless the process is stable, always look at a control chart
of the data first. Once statistical control is evidenced, then the histogram
and process capability may be analyzed.
Interpreting the Histogram
If
your data is from a symmetrical distribution, such as the Normal Distribution,
the data will be evenly distributed about the center of the data. If the
data is not roughly evenly distributed about the center of the Histogram,
it is commonly called "skewed". If it appears skewed, you should
understand the cause of the "skewness". Some processes will naturally
have a skewed distribution, and may also be bounded. If the variable is
waiting time, the lower bound may be physically limited to zero. See also:
Distributions Curve
Fitting
If double or multiple
peaks occur, look for the possibility that the data is coming from two different
sources, such as two separate personnel groups, or two differently adjusted
machines.
Remember that if the process
is out of control, then by definition a single distribution cannot
be fit to the data. Therefore, always use a control chart to determine statistical
control before attempting to fit a distribution (or determine capability)
for the data.
Interpreting the Capability
Indices
- Capability Indices
are only valid for processes in statistical control. See also Process
Performance
- Compare the non-normal
and normal indices. Capability Indices are quite sensitive to assumptions
of the distribution.
- A Capability index
is a statistic, subject to statistical error. (this error may be viewed
for a given set of data using the Capability Interval text box in the
Analysis Options dialog box). In a study by Pignatiello & Ramberg
(Process Capability Indices: Just Say "NO", ASQC's
47th AQC), a Monte Carlo simulation involving 1000 different trials
of 30 piece samples showed the following:
For true Cp=1.33:
55 trials calculated Cp
< 1.10 (5.5%)
196 trials calculated
Cp < 1.20 (19.6%)
For true Cp=1.00:
112 trials calculated
Cp > 1.20 (11.2%)
43 trials calculated Cp
> 1.30 (4.3%)
- Most practitioners
consider a Capable process to be one that has a Cpk of 1.33 or better,
and a process operating between 1.0 and 1.33 is "marginal."
Many companies now suggest that even higher levels of Cpk be maintained
by their suppliers. A Cpk exactly equal to 1.0 would imply that the
process variation exactly meets the specification requirements. Unfortunately,
if the process shifted slightly, and the out of control condition was
not immediately detected, then the process would produce output that
did not meet the requirements. Thus, the "extra" .33 allowed
for some small process shifts to occur that could go undetected. The
Table below provides an indication of the level of improvement effort
required in a process to meet these escalating demands, where "PPM
Out of Spec" refers to the average defect level measured in parts
per million.
Cpk
|
One-Sided
Spec
PPM Out of Spec
|
Two-Sided
Spec
PPM Out of Spec
|
0.25
|
226627
|
453255
|
0.5
|
66807
|
133614
|
0.7
|
17864
|
35729
|
- 0
|
1350
|
2700
|
- 1
|
483
|
967
|
- 2
|
159
|
318
|
- 3
|
48
|
96
|
- 4
|
13
|
27
|
- 5
|
3
|
7
|
- 6
|
-
|
|
2
|
0.00099
|
0.00198
|
See also:
When
to Use a Process Capability Chart
Calculations:
Cp
Cr
Cpk
Cpm
Process
Performance
|
