Video Transcript: Control Charts (Part 1)

Bob Lloyd, PhD, Executive Director Performance Improvement, Institute for Healthcare Improvement

In a previous session, we introduced the run chart. Now we want to start turning our attention to thinking about the control charts, which classically are known as “Shewhart Charts,” in honor of Dr. Walter Shewhart.

So you remember the run chart: We had an X and a Y axis. Time is always shown on the horizontal axis, and the measure of improvement — or our metric — is shown on the vertical, or Y axis. You can have patients, months, day, time, Monday, Tuesday, Wednesday all along the horizontal axis, whether you’re doing a run chart or a control chart. You remember the run chart was a plot of the data over time, and we put the median. Now the median — “x” with a tilde above it —gives us a center point; it’s also known as the fiftieth percentile.

What we’re going to do on the control chart, however, is we’re still going to have time on the horizontal, the measure of interest on the vertical; we’re going to collect our data, plot our dots; but now, instead of putting the median as the center line, we’re going to put the mean — which is shown as “x” with a line above it, otherwise known as “x-bar.”

Now, on the run chart, we didn’t have control limits. That’s one of the advantages of moving to a control chart. You end up getting what are called the “upper control limit” and the “lower control limit.” These two boundaries help to define the variation in the process. The tighter the variation, the tighter the control limits; the wider the variation, the further apart these are. You do not dictate or determine the upper and lower control limits. The variation that lives in the data determines how wide or narrow these lines are.

Now, one of the things to realize is that these upper and lower control limits are known by specific names. Classically they are called “sigma limits.” You will see them designated as “SL” in some software — sigma limits. Sometimes you’ll see a symbol: That’s sigma — which is a symbol in basic statistics — with a hat over it (the “hat” is an estimate), and this symbol, sigma, is often used to denote the standard deviation.

Well, these control limits are not standard deviations. That’s one thing to clearly remember. They are not standard deviations. They are sigma limits. The way that is shown is with this little hat saying that these limits are estimates of the dispersion in the data. The standard deviation is an estimate. The range — the difference between the min and the max — is also an estimate of the variation. The standard deviation is another way to detect variation. The key is that the standard deviation is a single number. It’s a statistic that’s trying to give you the average dispersion in a whole group of data. Control limits are actually boundaries of a process that keeps changing over time.

This is a fairly technical point but it’s not that difficult to grasp. The key thing is realizing that the standard deviation is not the same as the sigma limit. If you want to know more about that, what you need to do is grab a book on statistical process control, statistics, and it will go into greater detail. We don’t have time to cover that today.

Basically, the elements of the control chart look like a run chart, except we’re going to, again, replace the median with the mean. We get the upper and lower control limits that tell us the boundaries of variation in the data. We have data plotted over time, and we have our measure on the vertical.

Now, another thing to realize is that with a run chart, you can get away with less data than you can on a control chart. You can make a run chart with upwards of around 10 data points. When you move to a control chart, you need to have at a minimum about 15 data points, and preferably around 20. The reason being that the mean is more sensitive to point-to-point variation than the median. So we need to have a little bit more data.

Not think of this, if you’re collecting data monthly, you’re going to need 15 to 20 months of data before you can get enough data to make a chart. That’s why often times when we’re starting out with our improvement initiatives, we end up using the median and the run chart because we can start with a little bit of data, particularly if we’re just getting a project underway.

Those are the basic elements of the control chart and a little bit of the difference between a run chart. What we’re going to do in the next piece of this video is to describe how we actually analyze and interpret a control chart.