Topics: Control Charts, Minitab

Time and time again we see cases in which people identify that an outcome is undesirable. W. Edwards Deming’s classic text Out of the Crisis includes various anecdotes along these lines:

“The job in a certain staff area in a company that manufactures automobiles is to make monthly forecasts of sales. The men take into account many kinds of information. The forecast falls short or long, month by month, when compared with actual sales. The procedure for the next month had been to adjust the method up or down on the basis of this comparison. The reader may perceive that what the men were doing was guaranteeing that their method could never improve.“ (pp. 331-332)

Whether it’s sales numbers, the wait time at a doctor’s office, or the weight of a copper ingot—our customers want to fix the problem of the undesirable outcome. But without an understanding of whether the problem was caused by a special event or if the problem was inherent to the process that produced it, these fixes tend to make things worse if they have any effect at all. Control charts help people determine whether to address an undesirable outcome in one of two ways:

1. Special causes—fix a problem that affected a single outcome
2. Common causes—improve the process that creates all the outcomes

Control charts determine if a system is in-control. If the system is in control, then the spread and center of what you are measuring are predictable. It’s important not to confuse “predictable” with “good.” But it’s only after we know that a system is predictable that we can know what kind of changes to make so that a system can become good. When a system is in control, then the variation on the chart comes from common causes. (Using a control chart assumes that you can trust your measurements, but you probably already know all about Measurement Systems Analysis. If not, take a look at About Measurement Systems Analysis.)

## An in-control chart

Let’s look at a simple example. The following data show the proportion of unanswered calls to a call center. The proportions are plotted as a time series below:

Someone looking at the data might notice that the highest point is over 12%. They would say that it’s unacceptable for almost 1 out of every 8 incoming calls to go unanswered and that we must find the cause of this unacceptably high proportion. If they did, they would be chasing shadows.

Instead, let’s look at these data with a control chart. Use these steps to produce the chart yourself:

1. In Minitab® Statistical Software, open the dataset from https://support.minitab.com/en-us/datasets/control-charts-data-sets/unanswered-calls-data/
2. Choose Stat > Control Charts > Attributes Charts > P.
3. In Variables, enter ‘Unanswered Calls’
4. In Subgroup sizes, enter ‘Total Calls’
5. Click OK.

The resulting chart shows the following proportions from the subgroups:

The control chart shows that all the points fall within the control limits. Everything that’s happening in this system is predictable. In a predictable system, you will learn almost nothing by investigating the reason that any single point is high or low. The problem of unanswered calls here is due to common causes. Any improvement that does not address factors that are affecting the process all of the time is likely to be fruitless.

## An out-of-control chart

Here’s an example for a different case. The following data show the average length of a subgroup of 5 camshafts. The camshafts come from 3 different machines. Here are the means on a line plot:

The most noticeable points are the two high values for machine 3. It’s nearly irresistible to go investigate those points, but we can get even more information from control charts. Use these steps to produce the chart yourself:

1. In Minitab® Statistical Software, open the dataset from https://support.minitab.com/datasets/control-charts-data-sets/camshaft-length-data/
2. Choose Stat > Control Charts > Variables Charts for Subgroups > Xbar-R.
3. For the observations, enter ‘Machine 1'-'Machine 3’
4. In Subgroup sizes, enter ‘Subgroup ID’
5. Click OK.

Here, we’ll focus on the charts from machine 3 and machine 1. For machine 3, we see what we expected—the two high points are above the upper control limit. Because these points are out-of-control, a special cause likely affected those subgroups. We can go back and look at events around that subgroup and try to prevent the recurrence. When we do, the overall process should become more predictable.

On the line plot, it was much harder to realize that machine 1 is also out-of-control.

For machine 1, subgroup 8 is below the lower control limit. It’s worth noticing that machine 3 had an even lower value at subgroup 9, but that point was in-control because machine 3 has more variation than machine 1—possibly because of the special causes. We’ll need to investigate and fix the special cause for machine 1, too. Before we can begin to make overall process improvements on machines 1 or 3, we need to make sure that the process is predictable. If the machines are not predictable, then we won’t even know whether any changes we see are because of changes to the process or because the process does things we don’t expect it to do!

## The bottom line: why you need a control chart

Control charts tell you whether your process is in-control. If a process is out-of-control, then you need to fix special causes that affect the process intermittently. Once you fix those special causes, the process should be in-control and behave predictably. It’s only after a process is in-control that you can begin making changes to the overall process and know that the changes you see are because of the changes that you’re making, not because of the wild unpredictability inherent in the process. If you need to know whether you need to fix a process or whether you can improve a process, then you need a control chart.