Video Transcript: Control Charts (Part 2)

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

Let’s now take a look at how we actually analyze and interpret a control chart. You’ll remember we had our data plotted overtime. Time is on the horizontal axis, and our measure of interest is on the vertical. We’re going to have as our center line the mean (“x-bar”), and we’re going to have our upper and our lower control limits (“UCL,” “LCL”).

Now the way we start interpreting the control chart is that we place zones on the chart. There are three sigma limits above the center line, and there are three sigma limits below the center line. Most software will label these zones emanating from the center “C-B-A.” Same [above and below the center line], “C-B-A.”

Now that we have these zones, we can apply what are called the “test for special causes.” This is being able to look at the data and ask: Do I have special causes (things that knock a process out of whack)? Or do I have just what is called “random, common cause variation?” Typically data that vacillates between the upper and lower control limits is common cause variation. But there are ways to detect if you have special patterns in the data.

When we look at data that look like this line — it’s up, it’s down, it’s back and forth, and it’s between the upper and lower control limits — that’s a classic demonstration of what’s known as “common cause variation.” On the other hand, if we had a data point that went and exceeded the upper control limit, that’s a demonstration of “special cause” — that is, data that has exceeded the upper estimation of the variation in the process of the upper control limit (or, similarly, you could have data that exceeded the lower control limit).

Several of the other tests that we use statistically are whether or not there’s been a shift or a trend. Those are two classic ways to think about the data as they lay themselves out. A shift in the data occurs when you get a certain number of data points that hang above or below the center line. So, if we have our mean, and we had our data that went here, here, here and hung above the center line for eight or more data points in a row, that would signal a shift — that is, the data were randomly arraying themselves and stayed, for some reason, in a particularly high level or low level. You could have a shift up or a shift down. Eight data points or more constitute a shift in the process.

The other classic test that is used to apply statistical thinking to the chart is whether or not you have a trend. A trend is when you have six or more data points constantly going up or constantly going down. You would see data “one,” “two,” “three,” “four,” “five,” “six.” That would be an upward trend, and, similarly, you could have a downward trend. Note that if you have data points that go up, up, but then repeat, you don’t count the repeats, but what you do is see if in fact at some point they start going back up. If it goes up, up, repeat, and then drops, then that cancels the trend.

We have these two key tests, one is for a shift, and one is for a trend. Now, there are a couple other tests, and I’m just going to clean things up here a bit to show you what those look like.

We often times will look to see if we have data that form abnormal patterns. Let’s have our upper and our lower control limit with our mean. And then we have data that start arraying themselves around these zones. There are two key tests that we look at to understand whether or not data that fall even between the control limits are demonstrating abnormal patterns. The first one relates to how the data array themselves in these zones, and I’m going to again put the “C,” “B,” and “A” zones on here.

When you get two out of three data points in zone A or beyond, that’s a signal of a special cause. So here are two out of three data points. You could have it lay itself out like this, and you could actually have a third data point here. You still have two out of three in zone A of the chart. People say I understand where a data point that exceeds an upper or lower control limit is an extreme variation. Now you’re telling me that you can have patterns within a chart between the control limits that actually demonstrate special causes and abnormal patterns? The answer is yes.

Here’s a simple explanation. If I took the data and squished them all over, and I had over here a normal curve, as you move out this curve, you should see less data as you move out the tails of the distribution. The two out of three tests of a special cause is indicating you’re getting too much data bunching in the tails of your distribution.

The other test which relates to this is almost the converse. It’s when you get too much data bunching around the center. We would have data that essentially are random, and then all of a sudden 15 data points in a row hug the center line and then break out again. When you have 15 data points or more hugging the center line — that is falling between zone C (plus and minus one sigma on the other side of the mean) — this is a signal that there is too little variation. This gets to the fact that if we looked over here to our static display of data — you’ll remember from basic statistics that about 68 percent of the data fall between plus and minus one standard deviation of the mean on a normal curve — well, when you get a pattern like this, you’re exceeding the 68 percent; you’re getting too much data hugging this bell curve part of the distribution. That’s not a normal pattern. A random pattern, as we have said before, is just up and down, back and forth, and when you get a pattern like this — when you have random variation, very little variation, and then random again — that’s a signal that there’s something strange going on in the process itself.

We have these different rules, we have a trend, we have a shift, we have two out of three, and we have 15 or more hugging the center line. The classic rule that we started with is when you have a single data point that exceeds the upper or lower control limit, and that is classically known as a “three sigma violation of special cause.”

In a quick overview, that shows you how we use the special cause tests related to the zones on the chart. It gives you the ability to understand how we actually interpret the chart once we have it. Now we have actually built a control chart, we have plotted the elements of it — the mean, the upper and lower limits — and we now know how to interpret it.