QC Charts Example
1: Specifying Control Charts for Variables, Process Capability
example demonstrates how to specify control charts for variables in the
Control Charts module. It is based on the Cover.sta
data file. Open this data file via the File
Examples menu; it is in the Datasets
Let's assume that we are manufacturing plastic cover plates that have
to be integrated into an instrument panel. The width and the length (both
measured in millimeters) are important quality characteristics, since
the cover has to fit into a predefined frame. We will first use an X-bar
and R chart in order to monitor the width. At a later point we will create
a control chart for the length. Overall we have collected 20 samples of
3 observations each. Those data could have come directly from a measurement
device or from a database.
Specifying the Analysis.
Select Quality Control Charts
from the Statistics - Industrial
Statistics & Six Sigma submenu or from the Data Mining - Process Optimization - QC
Charts submenu to display the Quality Control
Charts Startup Panel. Then select X-bar
& R chart for variables on the Quick
tab (or the Variables
tab). Click the Real-time
tab and select the Auto-update
option button. Now click the OK
This will display the Defining
Variables for X-bar & R Chart dialog. On the Quick
tab, click the Variables
button and select the variable Width
as the Variable with measurements and
click OK. Enter a value of 3
in the fields for Constant sample size
and Minimum number of observations per
sample. This will ensure that STATISTICA
takes consecutive sets of three values and identifies them as belonging
to the same sample. Note that the Quality
Control module assumes that your data come from a measurement device
or database that takes samples of constant size from the on-going production
process. Therefore, specifying a sample identifier variable is optional.
Reviewing the Charts.
Click OK to produce the chart
and display the Results
Note that the chart is displayed as a stand alone window because of
the selection we made on the Real-time
tab of the Startup Panel. We could have chosen to display it in a
STATISTICA will produce a compound
graph that consists of an X-bar chart in the upper part (for monitoring
the process mean) and an R chart in the lower part (for monitoring process
variation). Both charts are accompanied by histograms that display the
distribution of the quality characteristics (sample means and ranges,
respectively). The dialog to the right allows you to control different
aspects of the control chart.
In general you need to ensure that the process variation is under control
before you can evaluate whether the process is "on target."
Therefore, we will inspect the control chart for the process variation
(R chart in this case) first. You will notice that the second sample is
out-of-control since the range for the second sample exceeds the upper
Now we turn to the X-bar chart. Here the 19th sample (not shown above)
seems to be out-of-control as it falls below the lower control limit.
In order to check for non-random patterns of adjacent samples we check
the runs rules tests. Click the Runs
tests button on the Charts
tab of the results dialog. This will perform runs rules tests with
the default settings. If you would like to change the settings for the
runs rules tests you can edit them by clicking the Runs
tests button on the Specs
tab of the results dialog to display the Runs Tests for Control
When you click the Runs tests
button on the Charts
tab of the results dialog, STATISTICA
will display two spreadsheets (one for the X-bar chart, one for the R
chart). Both spreadsheets indicate no runs rules violation (all cell entries
in the spreadsheet are OK).
If we know that our engineering specifications (tolerances) are +/-10
millimeters around the target width of 100, we can use this information
to perform process capability studies and have process capability indices
displayed in the graph.
On the X
(MA..)-specs tab click the Process
capability button to display the Specifications
for Capability Analysis dialog. Make sure the Type
is Nominal+-delta, enter 100
in the field for Nominal and
10 in the field for Delta.
Then click the OK (compute)
button. STATISTICA will display
two spreadsheets with process capability indices and process performance
By inspecting the process capability indices, we can conclude that the
process seems to be capable and centered overall (although we have out-of-control
conditions). You can also request a process capability histogram by clicking
the Histogram button under Process capability on the Charts tab.
Now, click the Options button
on the Results dialog to display the Options dialog and
select the Stats
tab. Under Include (display) capability
indices in graph, Normal select the check boxes for Cp,
Cpu, and Cpk.
Then click OK. The graph will
be updated and show the process capability indices in the upper left corner.
Note that you can also have the engineering specifications (upper and
lower spec limit) displayed in the X-bar chart. Click the Options
button and select the Show process specifications
and specification limits in chart check box on the Layout tab.
See also QC Chart Examples.