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Eston Martz

Statistics

Controls Charts Are Good for So Much More Than SPC

They help quantify probabilities and determine if results are statistically significant

Published: Tuesday, November 7, 2017 - 12:01

Control charts take data about your process and plot it so you can distinguish between common-cause and special-cause variation. Knowing the difference is important because it permits you to address potential problems without over-controlling your process.

Control charts are fantastic for assessing the stability of a process. Is the process mean unstable, too low, or too high? Is observed variability a natural part of the process, or could it be caused by specific sources? By answering these questions, control charts let you dedicate your actions to where you can make the most impact.

Assessing whether your process is stable is valuable in itself, but it is also a necessary first step in capability analysis. Your process has to be stable before you can measure its capability. You can predict the performance of a stable process and therefore improve its capability. If your process is unstable, by definition it is unpredictable.

Control charts are commonly applied to business processes, but they have great benefits beyond Six Sigma and statistical process control (SPC). In fact, control charts can reveal information that would otherwise be difficult to uncover.

Other processes that need to be in control

Let’s consider processes beyond those we encounter in business. Instability and excessive variation can cause problems in many other kinds of processes. 
• A test process that causes subjects to experience an impact of six times their body weight.
• A teacher’s process to help students learn. the material as measured by test scores.
• A diabetic’s process for maintaining blood sugar levels.

The first example stems from a colleague’s research. The researchers had middle-school students jump 30 times from 24-in. steps every other school day to see if it increased their bone density. Treatment was defined as the subjects experiencing an impact of six body weights, but the research team didn’t quite hit the mark.

My colleague conducted a pilot study and graphed the results in an X-bar S chart.

The fact that the S chart (on the bottom) is in control means each subject has a consistent landing style with impacts of a consistent magnitude—the variability is in control.

But the X-bar chart (at the top) is clearly out of control, indicating that even though the overall mean (6.141) exceeds the target, individual subjects have very different means. Some are consistently hard landers while others are consistently soft landers. The control chart suggests that the variability is not natural process variation (common cause) but rather due to differences among the participants (special cause variation).

The researchers addressed this by training the subjects how to land. They also had a nurse observe all future jumping sessions. These actions reduced the variability to the point that impacts were consistently greater than six body weights.

Control charts as a prerequisite for statistical hypothesis tests

Control charts can verify that a process is stable, as required for capability analysis. But control charts can be used similarly to test assumptions for hypothesis tests.

Specifically, the measurements used in a hypothesis test are assumed to be stable, though this assumption is often overlooked. This assumption parallels the requirement for stability in capability analysis: If your measurements are not stable, inferences based on those measurements will not be reliable.

Let’s assume that we’re comparing test scores between group A and group B. We’ll use this data set to perform a two-sample t-test as shown below.

The results indicate that group A has a higher mean, and that the difference is statistically significant. We’re not assuming equal variances, so it’s not a problem that group B has a slightly higher standard deviation. We also have enough observations per group that normality is not a concern. Concluding that group A has a higher mean than group B seems safe. 

But wait a minute… let’s look at each group in an I-MR chart. 

Group A’s chart shows stable scores. But group B’s chart indicates that the scores are unstable, with multiple out-of-control points and a clear negative trend. Even though these data satisfy the other assumptions, we can make a valid comparison between stable and an unstable groups.

This is not the only type of problem you can detect with control charts. They also can test for a variety of patterns in your data, and for out-of-control variability.

Different types of control charts

An Individuals and moving range (ImR) chart can assess process stability when your data don’t have subgroups. The X-bar S chart, the first one in this post, assesses process stability when your data does have subgroups.

Other control charts are ideal for other types of data. For example, the u-chart and Laney U’ Chart use the Poisson distribution. The p-chart and Laney P’ Chart use the binomial distribution. 

In Minitab Statistical Software, you can get step-by-step guidance in control-chart selection by going to Assistant > Control Charts. The Assistant will help you with everything from determining your data type, to ensuring it meets assumptions, to interpreting your results.

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About The Author

Eston Martz’s picture

Eston Martz

For Eston Martz, analyzing data is an extremely powerful tool that helps us understand the world—which is why statistics is central to quality improvement methods such as lean and Six Sigma. While working as a writer, Martz began to appreciate the beauty in a robust, thorough analysis and wanted to learn more. To the astonishment of his friends, he started a master’s degree in applied statistics. Since joining Minitab, Martz has learned that a lot of people feel the same way about statistics as he used to. That’s why he writes for Minitab’s blog: “I’ve overcome the fear of statistics and acquired a real passion for it,” says Martz. “And if I can learn to understand and apply statistics, so can you.”

Comments

XmR/ImR Chart Will Handle Most Service Industry Data

Wheeler and Pyzdek have both offered articles about how the XmR is the Swiss Army Knife of control charts. Master the XmR and you are well on your way to mastering ccontrol charts.

You don't have to know the decision tree for choosing the right control chart. QI Macros Control Chart Wizardl will automatically chose the right control chart based on your data.