A recent discussion on the Minitab Network on LinkedIn pertained to the I-MR chart. In the course of the conversation, a couple of people referred to it as "The Swiss Army Knife of control charts," and that's a pretty great description. You might be able to find more specific tools for specific applications, but in many cases, the I-MR chart gets the job done quite adequately.
When you're collecting samples of data to learn about your process, it's generally a good idea to group the sample data into subgroups, if possible. The idea is that these subgroups represent "snapshots" of your process. But what if you can't? Your process might have a very long cycle time, or sampling or testing might be destructive or expensive. Production volume may be too low. Or grouping your measurements might not feasibly capture variability for a given time. In many such instances, an I-MR chart is a good way to go.
What Can an I-MR Chart Do?Let's take a closer look at this "Swiss Army Knife" control chart and see what it does and how it works. The I-MR chart, like other control charts, has three main uses:
- To monitor the stability of your process.
Even the most stable process has variation in some amount, and attempts to "fix" normal fluctuations in a process may actually introduce instability. An I-MR chart can show you changes that should be addressed.
- To determine whether your process is stable enough to improve.
You generally don't want to make improvements to a process that isn't stable. That's because the instability keeps you from confidently assessing the impact of your changes. You can confirm (or deny) your process stability with an I-MR chart before you make improvements.
- To demonstrate process performance improvements.
If your improvements had a big impact, how do you show your stakeholders and higher-ups? Before-and-after I-MR charts provide powerful visual proof.
Now that we know what the I-MR chart can do, let's consider what it is. The I-MR is actually the combination of two different charts in a single presentation. The graph's top part is an Individuals (I) chart. It shows you the value of each observation (the individuals), and helps you assess the center of the process.
The graph at the bottom is called a Moving Range (MR) chart. It calculates the variation of your process using ranges of two (or more) successive observations, and plots them.
The green line represents the process mean and process variation on the I and MR portions of the chart, respectively, while the red lines represent the upper and lower control limits.
How to Create an I-MR ChartSuppose the chemical company you work for makes a custom solution, and you need to assess whether its pH value is consistent over time. You record a single pH measurement per batch. Since you are collecting individual samples rather than subgroups, the I-MR chart can help.
You record pH measurements for 25 consecutive batches. To prepare that data for the I-MR chart, just enter those measurements, in order, in a single column of a Minitab worksheet. (You can download this data set here to follow along. If you don't already have Minitab Statistical Software, you can use the free trial.)
Now select Stat > Control Charts > Variables Charts for Individuals > I-MR from the menu, and choose pH as the Variable. (If you have more than one variable you want to chart, you can enter more than one column here and Minitab will produce multiple I-MR charts simultaneously.) If you want to add labels, divide the data into stages, and more, you can do that in the "I-MR Options" subdialog.
Let's assume that we want to detect any possible special-cause variation. Click I-MR Options and select Tests. These tests highlight points that exceed the control limits and detect specific patterns in the data. In the dropdown menu, select "Perform all tests for special causes," and then OK out of the dialog.
Check the MR Chart First
After you press OK, Minitab generates your I-MR chart:
It might seem counterintuitive, but you should examine the MR chart at the bottom first. This chart reveals if the process variation is in or out of control. The reason you want to check this first is that if the MR chart is out of control, the I-chart control limits won't be accurate. In that case, any unusual points on the I chart may result from unstable variation, not changes in the process center. But when the MR chart is in control, an out-of-control I chart does indicate changes in the process center.
When points fail Minitab's tests, they are marked in red. In this MR chart, none of the individual points fall outside the lower and upper control limits of 0 and 0.4983, respectively. In addition, the points also have a random pattern. That means our process variation is in control, and we're good to take the next step: looking at the I Chart.
Check the I Chart After the MR ChartThe individuals (I) chart shows if your process mean is in control. In contrast to the MR chart, this I chart shows evidence of potential nonrandom patterns.
Minitab can perform up to eight different special-cause variation tests for the I chart. Problem observations are marked in red, and also display the number of the corresponding failed test.
This I chart shows that three separate observations failed two different tests. We can check the Session Window for more details about why Minitab flagged each point:
Observation 8 failed Test 1, which means this observation was more than 3 standard deviations from the center line—the strongest evidence that a process is out of control. Observations 20 and 21 failed Test 5, which tests for a run of two out of three points with the same sign that fall more than two standard deviations from the center line. Test 5 provides additional sensitivity for detecting smaller shifts in the process mean.
This I-MR chart indicates that the process average is unstable and therefore the process is out of control, possibly due to the presence of special causes.
After looking at your data in the I-MR chart, you know there may be a problem that needs to be addressed. That's the whole purpose of the control chart! The next step is to identify and address the source of this special-cause variation. Until these causes are eliminated, the process cannot achieve a state of statistical control.
If you'd like to know more about the behind-the-scenes math that goes into this chart, check out my colleague Marilyn Wheatley's post about how I-MR control chart limits are calculated.