## What is a Control Chart?

Control charts determine whether a process is stable and in control or whether it is out of control and in need of adjustment. Some degree of variation is inevitable in any process. Control charts help prevent overreactions to normal process variability while prompting quick responses to unusual variation. Control charts are also known as Shewhart charts.

A stable process operates within an ordinary, expected range of variation. It is predictable and consistent and is not influenced by special causes of variation, such as changes in the process itself, changes in the environment, or changes in the input materials or equipment. Stable processes are more likely to produce high-quality products or services. Conversely, an out-of-control process is unpredictable and more likely to make defects or errors.

A control chart displays process data by time, along with upper and lower control limits that delineate the expected range of variation for the process. These limits let you know when unusual variability occurs. Statistical formulas use historical records or sample data to calculate the control limits. Unusual patterns and out-of-control points on a control chart suggest that special cause variation exists.

Control charts can be valuable aids for tracking a continuous process and gaining insight into a newly established one. They can help with the following:

- Determine whether a process is stable.
- Find problems as they occur in an ongoing process.
- Assess the effectiveness of a process change.
- Predict the range of outcomes for a process.
- Assess patterns of special cause variation to identify non-routine events.
- Determine whether improvements should target non-routine events or the underlying process itself.

## Control Chart Example

Quality engineers at a manufacturing plant monitor part lengths. They use process data to create an X-bar-R chart, a control chart that evaluates both the process mean (X-bar) and spread (R chart for range).

Control charts typically contain the following elements:

- Data points representing process outcomes.
- Control limits depict the range of normal process variability.
- Centerline locates the process’s center value.
- Red dots indicate out-of-control points.

Learn more about Variability in a Dataset.

### Interpretation

For the part length example, we must ensure the R chart (bottom) is in control before analyzing the X-bar chart. If the R chart is unstable, the control limits for the X-bar chart will be invalid, potentially leading to false signals of an out-of-control situation on the X-bar chart.

The R chart does not flag any points in red. They’re all in control. However, the X-bar chart on the top is a different story because it flags six points. Red data points fail a statistical test and suggest that special cause variation exists.

Point 8 is out-of-control because it is below the lower control limit. But there are five more red points within the control limits. Why?

Control charts can test for various statistically improbable patterns.

The chart flags points 12, 13, 19, and 20 because 4 out of 5 points in a row are more than one standard deviation from the centerline on one side of the mean. That’s unlikely to occur by chance. Additionally, #17 is flagged because 2 out of 3 points are more than two standard deviations from the centerline on one side of the mean.

All the red dots suggest special cause variation exists because those patterns are unlikely to occur with only common cause variation. Assessing these patterns in conjunction with process knowledge might help us identify its source.

Learn more about the Mean, Standard Deviation, and Range.

## Types of Control Charts

Various types of control charts monitor different process properties over time. The following are standard control charts:

- X-bar: Average performance of a process using subgroups.
- I: Average performance without subgroups.
- R: Variation (range) of a process with subgroups.
- S: Variation (standard deviation) with subgroups.
- MR: Variation (moving range) without subgroups.
- C: Number of defects in a subgroup.
- P: Proportion of defective products.
- U: Number of defects in a unit of product or service.

Control charts for continuous data, such as lengths and weights, typically have two panels. The top panel assesses the process mean over time, while the bottom evaluates its variability. In this manner, X-bar-R, X-bar-S, and I-MR charts are common pairings because they assess both the mean and variability.

Control charts for attribute data, such as pass or fail for defect data, have only one panel and evaluate either the proportion of defects or the number of defects per subgroup.

While analysts frequently use control charts for quality improvement projects, learn how it can be helpful Using Control Charts with Hypothesis Tests.

Mark says

What, if anything, can be learned by generating a control chart from 30 consecutive samples pulled originally to generate a capability study.

Jim Frost says

Hi Mark,

Typically, you should create a control chart before performing a capability study. You need to know that your process is in statistical control (i.e., predictable). If it’s not in control, the capability results are meaningless.

At any rate, you should be able to create an I-MR chart using those 30 consecutive samples. However, they usually recommend at least 100 samples for those charts. But you’d get some preliminary information at least.