Control limits

Control limits are upper and lower bounds set on a process or quality characteristic in order to ensure that it stays within a certain range. They are used in statistical process control (SPC) to monitor a process and detect when it is operating out of control. When a process goes outside of the control limits, it is an indication that there may be a problem with the process and further investigation is needed. The control limits are typically calculated based on historical data and are used to detect abnormal or unexpected variations in the process.

Interpretation of control limits

When interpreting control limits on a chart, it's important to consider the context of the process and the goals of the monitoring and control system.

If a process is operating within the control limits, it means that the process is stable and predictable and that any variations seen in the data are due to common causes of variation. However, if the process is operating outside of the control limits, it means that the process is not stable and predictable, and that there may be an assignable cause of variation.

If a point on the chart crosses the upper control limit (UCL) or lower control limit (LCL), it's an indication that the process is operating out of control. This means that there's an assignable cause of variation that needs to be investigated. Crossing the UCL or LCL doesn't mean that the process is inherently bad, but it's a signal that something is different and needs to be investigated.

If there is a pattern of points crossing the control limits, it's a signal that there may be a consistent issue with the process and further investigation is needed. If there is no clear pattern, but just one or two isolated points crossing the limit, it could indicate random or sporadic issues and the process is still in control.

It's important to note that control limits are based on historical data and are not necessarily a guarantee of future performance. Therefore, it's necessary to investigate any out-of-control points and make any necessary adjustments to the process to bring it back into control.

Control limits calculation

There are several methods for calculating control limits, but one common method is to use statistical process control (SPC) charts. The most common types of SPC charts are the X-bar chart and the R chart.

To calculate the control limits for an X-bar chart:

1. Collect a sample of data from the process. The sample size should be at least 30.
2. Calculate the mean (X-bar) of the sample data.
3. Calculate the standard deviation (s) of the sample data.
4. Use the following formulas to calculate the upper control limit (UCL) and lower control limit (LCL) for the X-bar chart:

UCL = X-bar + A2 * (s/sqrt(n))

LCL = X-bar - A2 * (s/sqrt(n))

where A2 is a constant that depends on the sample size, n, and the confidence level.

To calculate the control limits for an R chart:

1. Collect a sample of data from the process. The sample size should be at least 30.
2. Calculate the range (R) of each sample.
3. Use the following formulas to calculate the upper control limit (UCL) and lower control limit (LCL) for the R chart:

UCL = D4 * R-bar

LCL = D3 * R-bar

where R-bar is the average range and D3 and D4 are constants that depend on the sample size and the confidence level.

It's important to note that these are just examples of the methods, and there are other methods as well, such as using the standard deviation instead of the range, or using other probability distributions.

Other types of limits

There are several other types of limits that are similar to control limits and are used for monitoring and controlling processes. Some examples include:

• Specification limits: These are the upper and lower limits set by the customer or industry standards for a process or quality characteristic. They define the acceptable range for the process and are used to determine if the process is producing acceptable products or services.
• Action limits: These are limits that are set slightly outside of the control limits, and are used to trigger an action when the process goes outside of them. This could be an adjustment to the process or an investigation to determine the cause of the problem.
• Warning limits: These are limits that are set further out from the control limits than the action limits, and are used to indicate that the process is trending towards going out of control.
• Target limits: This are limits that are set to represent a desired or optimal level of performance for a process or quality characteristic.
• Statistical Process Control (SPC) limits : these limits are calculated based on the statistical properties of the process and are used to detect when the process is operating out of control.

It's important to note that the type of limit used will depend on the specific process and the goals of the monitoring and control system.

Control limits — recommended articles

P chart — Control chart — CUSUM chart — Common cause variation — Attribute control chart — Np chart — Acceptance sampling — Interval scale — Cluster analysis

References

• Steiner, S. H. (1999). EWMA control charts with time-varying control limits and fast initial response. Journal of Quality Technology, 31(1), 75-86.
• Hoskisson, R. E., & Turk, T. A. (1990). Corporate restructuring: Governance and control limits of the internal capital market. Academy of management Review, 15(3), 459-477.
• Hillier, F. S. (1969). X-and R-chart control limits based on a small number of subgroups. Journal of Quality Technology, 1(1), 17-26.