# Introduction to Control Charts: What They Are, How They Are Used and a Control Chart Example

## About Control Charts

In simple terms, a control chart is a plot of data that includes statistical limits. These limits represent the variation in the data that is inherent within the process itself. This is known as common-cause variation: variation between data points which is not due to special circumstances that differentiate one point from another. The limits represent the range of values that can be expected if the process operates without any special external circumstances affecting the data.

Keep in mind that control limits are not the same as specification limits. Control limits are calculated from the data itself, whereas specification limits represent the customer requirements. Since control limits are derived from the data, it is important to have enough data points before calculating control limits. Experts typically recommend at least 13 data points, although 20 or more is even better.

The most basic type of control chart is the individuals chart, which is also the most popular. Each measurement is a separate data point and the control limits are calculated using a formula based on the mean of the data set and the median moving range. (The moving range is the set of differences between consecutive points.) Most data can be charted using the individuals chart, although for some types of data other chart types are more powerful. The main requirement for the individuals chart is that the data must be normally distributed, in the typical bell-shaped curve that is symmetrical and has the same mean, median and mode. The data can be tested to ensure it means the normality requirement. If data is not normal, it may be possible to transform the data, calculate the limits on the transformed data and then reverse-transform the limits.

In the control chart shown here, none of the data points lie outside the control limits. This means that all of the variation in the data is common cause variation; nothing particular was different in any specific instance, and no attempt should be made to understand why one data point is higher or lower than any other. In addition, assuming that conditions do not change and in the absence of special cause, the data will continue to fall within the control limits, making process performance predictable.

One popular use of control charts in Six Sigma DMAIC projects is determining whether the control limits change after process changes are implemented during the Improve phase. If improvements are successful, control limits should be closer together, indicating less variation, and the center line (representing the average of the data) should move in the desired direction. One control chart can be created showing before-and-after data, with separate control limits for the two phases to show the change.

Another use of control charts is for process management outside of projects. Certain patterns in the data can be an early warning sign that something has changed in the process that affects performance. This may be a factor inherent in the process, representing common cause or it may be one or more special causes. In either case, leaders need to understand which type of variation is present in order to respond in the appropriate way.

Control charts can also be analyzed in other ways to gather information about process performance and variation. For instance, they can be used to detect when a process shift is occurring, as evidenced by a series of points all on the same side of the center line, or a series of points in a row increasing or decreasing. Software programs such as Minitab can be used to create control charts and test for special cause.