Control limits are the boundaries of variation that indicate whether a process is stable or not. They are based on statistical calculations and help us monitor and improve the quality and performance of a process.

## What is a Control Limit?

A control limit is a horizontal line on a control chart that marks the point beyond which a sample value is considered a special cause of variation. A special cause of variation is an unusual or unexpected event that affects the process output, such as a machine breakdown, a human error, or a change in the environment. A sample value that falls outside the control limits indicates that the process is out of control and needs to be investigated.

There are two types of control limits: upper control limit (UCL) and lower control limit (LCL). The UCL is the highest value that a sample can have and still be considered normal. The LCL is the lowest value that a sample can have and still be considered normal. The distance between the UCL and the LCL is called the control width, and it represents the range of acceptable variation in the process.

The control limits are calculated from the data that is plotted on the control chart. They are usually placed at +/- 3 standard deviations from the centre line, which is the average of the sample values. This means that 99.73% of the sample values should fall within the control limits, assuming that the process follows a normal distribution. However, the control limits can be adjusted depending on the type of control chart, the sample size, and the desired level of confidence.

## How to Calculate Control Limits

There are different methods to calculate control limits depending on the type of control chart and the type of data. For example, for a variable control chart, which measures continuous data such as length, weight, or time, the control limits are based on the mean and the standard deviation of the sample values. For an attribute control chart, which measures discrete data such as defects, errors, or failures, the control limits are based on the proportion or the count of the sample values.

One of the most common types of variable control charts is the X-bar and R chart, which plots the mean (X-bar) and the range ® of each sample. The control limits for the X-bar chart are calculated as follows:

- UCL = X-bar + A2 * R
- LCL = X-bar – A2 * R

Where X-bar is the average of the sample means, R is the average of the sample ranges, and A2 is a constant that depends on the sample size. The control limits for the R chart are calculated as follows:

- UCL = D4 * R
- LCL = D3 * R

Where R is the average of the sample ranges, and D4 and D3 are constants that depend on the sample size. The values of A2, D4, and D3 can be found in statistical tables or calculated using software.

## How to Use Control Limits

Control limits are used to monitor and improve the quality and performance of a process. By plotting the sample values on a control chart and comparing them with the control limits, we can see whether the process is stable or not. A stable process is one that only has common causes of variation, which are the expected sources of variation that are inherent. A stable process is predictable and consistent, and it meets the customer’s requirements.

Suppose a sample value falls outside the control limits. In that case, it means that there is a special cause of variation, which is an abnormal and unexpected source of variation that affects the process output. A particular cause of variation is a sign of a problem that needs to be identified and eliminated. A process that has special causes of variation is unstable and unpredictable, and it does not meet the customer’s requirements.

To use control limits effectively, we need to follow these steps:

- Collect data from the process and plot it on a control chart.
- Calculate the control limits and draw them on the control chart.
- Analyze the control chart and look for any sample values that fall outside the control limits or any patterns that indicate instability, such as runs, trends, or cycles.
- Investigate the causes of any out-of-control points or patterns and take corrective actions to eliminate them.
- Continue to monitor the process and update the control limits as needed.

## Conclusion

Control limits are the boundaries of variation that indicate whether a process is stable or not. They are based on statistical calculations and help us monitor and improve the quality and performance of a process. By using control limits, we can identify and eliminate the special causes of variation that affect the process output and cause customer dissatisfaction. Control limits are a powerful tool for quality improvement and process excellence.