Quality Tools – Run Charts – Part 4: Runs

This post is part 4 in our series on run charts. This one addresses the run chart rule for runs. It shows how having too many or too few instances of crossing the centerline of the run chart can signal special cause variation.
(Duration = 5 min. 19 sec.)


This is part 4 in our series on run charts. In part 1, we learned about run charts in general and why they are so helpful in seeing how process performance changes over time. We also learned how to determine if the variation we see in the performance is just common, normal everyday variation or if the variation we see indicates that something different, something special, is going on that indicates process performance has fundamentally changed. We learned that run chart rules can be used to help us detect those statistical signals of process change. In part 2, we learned about the run chart rule for detecting trends. In part 3, we learned the rule for detecting a shift and here in part 4, we will learn about another run chart rule – this one is for runs.

When the variation we see in a run chart is just the common everyday -stuff- or -noise- going on in the background, we would expect that the data is going be above the centerline sometimes and below the centerline sometimes. Sometimes a few data points in a row might fall above, sometimes a few below and as a result, if the process is truly random, we would also expect that the run chart line would cross the centerline within a certain frequency. If it crosses the centerline too often, it suggests something unusual is going on. It’s a statistical signal for special cause variation. Same goes for not crossing the centerline often enough. That’s a statistical signal for special cause variation too. So how do you know how often is too many or too few? – with a run chart rule of course!

To apply the run chart rule for runs, we count the number of runs. A -run- in this context is a series of consecutive data points above or below the centerline. The easy way to count the number of runs there are on a run chart or a section of a run chart, is counting how often the line that connects your data points CROSSES the centerline – and then add one. We can then use a table that lists the number of data points that are in your run chart or run chart segment that DO NOT fall on the centerline, and then see how many runs are considered too few and how many runs are considered too many to suggest that non-random or special cause variation isn’t going on.

So let’s look at a quick example. On this view of the graph, just consider the section of the run chart on our screen. There’s 27 data points. We’ll count the number of times the data line crosses the centerline. It crossed the centerline 13 times and then we add one, as I mentioned earlier. That gives us 14 for the number of runs.

Now we look at a table of values for the run chart rule for runs. We have 27 data points in the section we are analyzing and the table tells us that the lowest number of runs we would expect to see if the variation is random is 10. The highest number of runs we would expect to see if there just random variation in a series of 27 data points is 19. Our count of 14 falls inside those limits so this section of the run chart does not seem to have special cause variation, at least on the basis of the run chart rule for runs.

Let’s look a different section of the run chart. Starting at data point 151 and going to data point 180, we have 30 data points. None of them fall on the centerline, so 30 is count for the number of data points we will use on the table. Now let’s count how often the centerline is crossed. It crosses the centerline 10 times and we will add one to the count and that gives us 11 for the number of runs. So, let’s look at the table of values for runs. In the row on the table for 30 data points, we see that if there is only common cause variation, we should have a value of 11 or greater on the low end and 21 or lower on the upper end. Our value is 11, so this run chart section meets the criteria for only showing common cause variation – on the basis of the number of runs.

So, that’s how to apply the run chart rules for runs. In the next video, we will look at the last of the four run chart rules – for outliers.

On the ImproveTheSystem.com website page where this vlog is embedded, scroll down to see some notes and links to other resources that expand on the topic just presented. A complete transcript of what’s presented here is also provided on that page.

If you have any questions or comments, please contact me directly at M I C Mic at Improve The System.com. I will do my best to reply to every inquiry.

Thanks for watching!

Notes and Resources

  • An excellent summary article on use of run charts and application of run chart rules in healthcare – Perla RJ, Provost LP, Murray SK: The run chart: a simple analytical tool for learning from variation in healthcare processes. British Medical Journal – Quality and Safety. 2011;20:46. e51. doi:10.1136/bmjqs.2009.037895. https://goo.gl/MaEcCL
  • Posted September 2018