The two control
charts most often associated with statistical
process control, (SPC), are the X-Bar
and Range or R charts.
X-Bar is just a fancy word for mean, also known as average. Range
charts are just that, the range that the sample lay between. You
should always set up the Range or R-Bar control
The charts are compared with control limits. Control limits, are
typically calculated based on the number of original samples, or first
samples, taken on any given process. (see upper
control limit, lower
control limit and Pre-Control
Limit) The number of samples to start with will vary based on
any given process, but should be sufficient to represent the
population of the widget being manufactured. Motorola in the 1980ís
require their suppliers to supply 75 pieces of data for first article
Once you have taken the data using a stratified
sampling plan, the control limits are established by using a
factor scale that will estimate the sigma, or standard deviation.
Using this estimate, you can add and subtract 3 times one sigma to get
your control limits and zones.
Remember that the bell of a bell
shaped curve is +/- 3 sigma. A different factor is used for the range
control limits. Note that if the number of observations are less than
7, then the lower control limit on the range charts is always zero,
(0). For more information on how to calculate upper control limits and
lower control limits, including the factor tables, see our glossary.
Once you have established your control limits, periodically you take
more samples, usually 2 to 5 more sample pieces, and calculate the
mean and range and plot them on the chart.
For additional information see ZeroRejects
and Statistical Process Control, (SPC)
A typical X-Bar chart should show a
saw toothed pattern when the data points are connected as seen below.
Note that the control limits are the top most and bottom most line on
the chart below.
To create the zones, first find the
upper and lower control limits and then divide the section of the
chart between the UCL, (upper control limit), and the mean and
the LCL, (lower control limit), and the mean evenly. You do not
calculate the zones individually.
|zone A = mean +/- 3 sigma
zone B = mean +/- 2 sigma
zone C = mean +/- 1 sigma
The established way to trend these charts is by
using the WECO, (Western
Electric Company), rules
ARE OUT OF CONTROL IF . . .
- A single point falls outside the
3 Sigma limit, i.e. beyond Zone A
- Two out of three successive
points fall in Zone A or beyond, the odd point may be anywhere
- Four out of Five successive
points fall in Zone B or beyond, the odd point may be anywhere
- Eight successive points fall in
Zone C or beyond
For additional information see What
are the WECO rules for signaling "Out of Control"?
Another way to envision the zones are shown below.
There are many different rules that one could
use. These type of rules are to evaluate trends. Since every process
can be different, the rules are sometimes modified as to not stop
production for an out of control condition when the design margin is
still being adhered to.
limits are sometimes used instead of the calculated upper
control limits for control
charts. This is done due to the fact that some processes may
typically run skewed, or shifted from the mean or median. There are
established formulas to calculate pre-control, but as with all cases,
to include the WECO rules, you may have to modify them to fit you
you can easily see where your data is in relation to your
specification and design margin.
For addition information...
Charts as a Tool in Data Quality Improvement (U.S. Department of
* Reference Quality
Planning and Analysis - Juran/Gryan