Every process varies. If you write your name ten times, your
signatures will all be similar, but no two signatures will be
exactly alike. There is an inherent variation, but it varies
between predictable limits. If, as you are signing your name,
someone bumps your elbow, you get an unusual variation due to
what is called a "special cause". If you are cutting diamonds,
and someone bumps your elbow, the special cause can be expensive.
For many, many processes, it is important to notice special
causes of variation as soon as they occur.
There's also "common cause" variation. Consider a baseball
pitcher. If he has good control, most of his pitches are going to
be where he wants them. There will be some variation, but not too
much. If he is "wild", his pitches aren't going where he wants
them; there's more variation. There may not be any special causes
- no wind, no change in the ball - just more "common cause"
variation. The result: more walks are issued, and there are
unintended fat pitches out over the plate where batters can hit
them. In baseball, control wins ballgames. Likewise, in most
processes, reducing common cause variation saves money.
Happily, there are easy-to-use charts which make it easy see
both special and common cause variation in a process. They are
called control charts, or sometimes Shewhart charts, after their
inventor, Walter Shewhart, of Bell Labs. There are many different
subspecies of control charts which can be applied to the
different types of process data which are typically
All control charts have three basic components:
- a centerline, usually the mathematical average of all the
- upper and lower statistical control limits that define the
constraints of common cause variations.
- performance data plotted over time.
Things to look
The point of making control charts is to look at variation,
seeking special causes and tracking common causes. Special causes
can be spotted using several tests:
- 1 data point falling outside the control limits
- 6 or more points in a row steadily increasing or
- 8 or more points in a row on one side of the centerline
- 14 or more points alternating up and down
In those charts that pair two charts together, you will want
to look for these anomalies in both charts.
The simplest interpretation of the control chart is to use
only the first test listed. The others may indeed be useful (and
there are more not listed here), but be mindful that, as you
apply more tests, your chances of making Type I errors, i.e.
getting false positives, go up significantly.
Types of errors:
Control limits on a control chart are commonly drawn at 3s
from the center line because 3-sigma limits are a good balance
point between two types of errors:
- Type I or alpha errors occur when a point falls outside the
control limits even though no special cause is operating. The
result is a witch-hunt for special causes and adjustment of
things here and there. The tampering usually distorts a stable
process as well as wasting time and energy.
- Type II or beta errors occur when you miss a special cause
because the chart isn't sensitive enough to detect it. In this
case, you will go along unaware that the problem exists and thus
unable to root it out.
All process control is vulnerable to these two types of
errors. The reason that 3-sigma control limits balance the risk
of error is that, for normally distributed data, data points will
fall inside 3-sigma limits 99.7% of the time when a process is in
control. This makes the witch hunts infrequent but still makes it
likely that unusual causes of variation will be detected.
If your process is in control, is that good
enough? No. You have to start by removing special causes, so that
you have a stable process to work with. But then comes the real
fun, and often the most substantial benefits: it is time to
improve the process, so that even common cause variation is