This is part of a series of blog posts on measurement for improvement. You can read them all here.
Many authors and consultants join me in arguing for collecting data over time and displaying it in a time series chart like a run chart. Some also advocate for the added benefit and sensitivity of using a Shewhart SPC chart. But some of these advocates also recommend you only need one type of Shewhart SPC chart when there are different types of charts for different kinds of data. Let’s unpack this a little.
Data over time in a Run Chart
For beginners and those just launching a project, the simple run chart is the data display tool of choice. This is the tool taught in most education and healthcare improvement trainings around the world. It’s a simple tool, doesn’t require a lot of data and skill, can be built on paper or in Excel, and has four rules to help identify non-random signals. For a large cohort of improvers, this is all they use. It’s definitely better than static tables and before-and-after comparisons, but it does not help differentiate common from special cause and is not as sensitive to detect changes as Shewhart SPC charts.
The Individuals Chart
Enter the Individuals Chart (also known as the I-chart or Xmr chart). The I Chart is a basic Shewhart SPC charts and can feel like an extension of the run chart. I Charts are for continuous (variable) data and focus on single value subgroups. The moving range between points is used to calculate the limits.
In the opening I mentioned some authors and consultants advocate for Shewhart SPC charts over plain data or run charts and recommend “Process Behavioral Charts,” a term coined by Dr. Donald Wheeler to describe the I Chart. Dr. Wheeler is the author of an accessible and short book Understanding Variation: The key to managing chaos (2nd Ed) and makes a strong argument for using Shewhart charts to understand the variation in data to distinguish between common and special causes. He only uses the I Chart in this particular book. In the appendix (and other writings), he makes the case that the I Chart is sufficient for most data and that other chart types (ex, attribute data charts) are problematic because they require the user to “verify the probability model” which most folks are not able to do. His recommendation has resulted in adoption and advocacy of the I Chart exclusively.
Important consideration when using I Charts
While the I Chart is one of the most basic Shewhart Charts, there are a few important things to appreciate.
- The I Chart rely on the moving range to calculate the limits. To avoid issues, it’s recommended to have a minimum of 20 subgroups (20 points) before calculating limits.
- To calculate the limits appropriately, I Charts require screening the moving range for special cause to avoid inflation of the limits and reducing your ability to see special cause. Many free Excel templates and some consumer software do not perform this screening.
- The I Chart is less sensitive than other charts and may not show special cause that more appropriate charts for the data will show.
Case Example: C chart vs I Chart
Let’s look at an example of patients admitted with an adverse drug event (ADE) while in the hospital. Thanks to Cliff Norman of Associates in Process Improvement for this example (and many others). Let’s start by looking at these monthly counts of ADEs in a run chart.
Figure 1. Run Chart
Remember the run chart uses a median as the centerline. Reviewing these data and considering the run chart rules for non-random signals, you note there is a shift of 6 data points below the median (January is on the median and does not break the shift).
Now let’s look at these data in an I Chart.
Figure 2. I Chart
In an I Chart, we move to the mean as the centerline, and then the point-to-point moving range is used to help calculate the upper and lower control limits. Using the rules for special cause, this chart shows no special cause present. At first pass, this may bring relief that the more sensitive I Chart helped you avoid tampering in a process that is actually stable.
Adverse drug events are a type of error (also known as nonconformities). They are attribute data, and in this case, a count each month. The data collection method leads to an area of opportunity is the same each month (n=300). Using the Shewhart Chart Selection Guide, these data would be best suited by a C Chart.
Figure 3. Basic Shewhart Chart Selection Guide (HCDG, Figure 56.1, p. 151)
Let’s look at these data in a C Chart.
Figure 4. C Chart
Wow! What happened? The red dots are my software warning me that special cause exists. In this case, Rule 1 (points outside the limits) and Rule 4 (two out of three points in the outer one-third) are present.
Note in comparing the I Chart and the C Chart, the difference in the limits. The I Chart has much wider limits based on the point-to-point moving range. The C Chart, which is the recommended chart for this type of data, uses a different theory and formula and results in more sensitive limits. In this example, the I Chart would have led us to believe we had a stable process when the C Chart shows we have special cause.
Shewhart Chart Selection
The I Chart is a basic and versatile chart. There are times it is the right chart (single value continuous data) or you are presented with data that can only be displayed in an I Chart (rates or percentage data where you only have the final value). It’s important to appreciate the I Chart is not as sensitive as other charts; it requires more data to calculate limits (20 points), and templates and software may not properly screen out special cause in the moving range. With a little understanding about the best way to measure what you are trying to improve and using a low cost Excel macro, you can pick the Shewhart Chart that is most appropriate. It also opens the door to a deeper level of understanding variation through Shewhart’s theories.
Want to learn about Shewhart Charts and measurement for improvement? Check out my favorite book by Lloyd Provost and Sandy Murray called The Health Care Data Guide: Learning from Data for Improvement. Not in health care? Don’t worry. It’s still the best reference for improvement data and measurement out there.
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