One of the fundamental tools of quality improvement is being able to make a run chart to understand the variation In your process over time. A run chart is very simple. On the x-axis, we have data in some sort of chronological order, for example Monday, Tuesday, Wednesday, it could be January, February, March, and on the y-axis we put our measure, I'm just gonna call it M, measure of interest. And that could be a percent, it could be a count, could be money. We get the data in chronological order, and we plot them. We connect the dots with a line. And then we need to start figuring out how to interpret this chart. Well, we do that with several simple steps. The first step is to put a center line through the middle of the plotted dots. And this center line, sometimes called CL, for a run chart, is what's called the median. Now, the median is also known as the 50th percentile. It is shown mathematically as an x with a little tilde above it. We have the data plotted in time sequence, we have our center line, a form of the average, if you will, but it's the median for the run chart. Now what we're going to do is define a run. What is a run? Now, a run is one or more data points on the same side of the median. So here we have one data point, here we have one. One, one, one. But here we have one, two, three, four data points. A run can be one or more data points on the same side of the center line. That's the key. It's as the data flip and flop back and forth across the center line, we count how many dots end up in a little cluster. Here we have one, one, one. Here we have three. Maybe two here, one, one. So we get the number of runs, and then we're going to be able to interpret the chart. And we do that by using a series of simple run chart rules. Now, there are many run chart rules that people have used over time. And you will see different people using different rules. Here at the IHI, we have what we call the four simple run chart rules. They are basically, a shift in the data, a trend in the data, whether you have too many or too few runs, and finally, an astronomical data point. And let me explain each of these quickly. A shift in the data is when you have too much of the data hanging above or below this median center line. And the way we make this determination is if you have six or more data points hanging in a group above or below the center line, that's an indication of a shift, that the data had moved to a level and stayed there too long. So you have random and all of a sudden you have one, two, three, four, five, six, and then it goes random again. This run of six data points in a row above the center line signals a shift. And the data have hung there for too long when they should be just randomly flipping and flopping. And you can see that there could be a shift downward as well. The second one is a trend. And while some people think that this is a downward trend, or this is an upward trend, two data points does not make a trend. What we're looking for to get a statistical trend in the data is to have five data points constantly going up or constantly going down. Now, if you had data points that went up, up, up, repeat, repeat, repeat, but kept going up, you don't count the repeats, but as long as it continued its upward journey, or downward journey, it's still a trend. If it went up, up, up, equal, equal, then dropped, then the trend would be canceled, all right? But a trend, and this is one a lot of people struggle with, five or more data points constantly going up, or constantly going down. Third one requires a table. What you do is you find out how many runs you have on your chart, and then you look up in this table for the total number of data points, and what was the low number of runs and the high number of runs? And for a given number of data points, say, 20 data points, it'll tell that you should have no fewer than x number of runs, and no more than y. And the idea here is that if data are randomly arrayed, you should see just some sort of random flipping and flopping back and forth. If you get data again that are hanging, on one side or the other, and you only have two runs in your data, you're gonna have not enough data that forms essentially a normal distribution. So this table which has been figured out mathematically for years, is designed to tell you how much variation there should be in a given set of data. So if you had 15 data points, 20, 30, it will tell you the lower and upper boundaries of the number of runs. The final test, or rule, if you will, is whether or not we have an astronomical data point. Now, this is a judgement call, something I refer to as the interocular test of significance. We have data that are going along, and then all of a sudden, wonk, we've got this huge spike, and we wonder why. Well, often times two things. One, we could have collected the wrong data, that for some reason, data got into our data set that shouldn't have been there, cuz here's where the bulk of the data typically fall. Or, in fact something, special was going on on that day. If this is food trays being deliver to the medical units, and this is the day that the elevator people came and shut down three banks of elevators, when all the food trays backed up. And if you're looking a percent of food trays delivered on time, you'd see this big spike. Well, an astronomical data point is not a statistical determination on a run chart, it's an eyeball test. And it's guidance that you should either look at your data or put the data on a control chart, which will be in a subsequent session to find out if in fact that is truly different than the rest of the data. So there you have it. The run chart in a nutshell. You've got the elements, x- and y-axis, the median, plot the data over time, figure the number of runs, and then apply the four simple run chart rules.
