Control Limits: A Comprehensive Guide to Setting and Utilizing Them

Control limits play a crucial role in control charts, distinguishing them from simple line graphs or run charts. They serve as boundaries that help determine whether a process is stable and predictable or not. This article delves into the concept of control limits, exploring their significance, calculation methods, and applications in process monitoring and improvement.

Key Facts

  1. Control limits are calculated from the data plotted on a control chart. They are placed +/- 3 sigma away from the average line.
  2. Control limits are used to distinguish between common cause variation and special cause variation. Common cause variation refers to the natural variation that is inherent in a stable process, while special cause variation indicates an unusual or unexpected event.
  3. Control limits provide a guide to what is happening in a process and help in understanding the expected variation.
  4. Control limits take into account both within-sample variation and between-sample variation. For example, in a control chart for the average and range, the range represents within-sample variation, while the average represents between-sample variation.
  5. The choice of setting control limits at +/- 3 sigma is based on the work of Walter Shewhart, who conducted extensive research and experiments to determine the optimal limits. These limits balance the probability of making two types of mistakes: calling common cause variation a special cause and calling special cause variation common cause.
  6. Control limits are not probability limits. They are designed to work best at +/- 3 sigma and are not associated with any exact probability of looking for trouble.
  7. There are different formulas for calculating control limits depending on the type of data being plotted on the control chart. The formulas vary for different types of control charts such as c, p, u, np, individual moving range XmR, XbarR, and XbarS charts.

Significance of Control Limits

  1. Distinguishing Common Cause and Special Cause Variation

    Control limits enable the differentiation between common cause variation, which is inherent in any stable process, and special cause variation, which indicates an unusual or unexpected event. This distinction is essential for identifying and addressing assignable causes of variation, leading to process improvement.

  2. Providing a Guide to Process Behavior

    Control limits offer a valuable guide to understanding the expected variation within a process. They establish a range within which the process is considered to be in control, allowing for the identification of significant deviations that require investigation.

  3. Accounting for Within-Sample and Between-Sample Variation

    Control limits encompass both within-sample variation and between-sample variation. For instance, in an average and range control chart, the range represents within-sample variation, while the average represents between-sample variation. This comprehensive approach provides a more accurate assessment of process stability.

Calculating Control Limits

The calculation of control limits varies depending on the type of data being plotted on the control chart. Some common formulas include:

  1. p Chart

    UCL = p + 3√(p(1-p)/n)

    LCL = p – 3√(p(1-p)/n)

  2. Individual Moving Range Chart (XmR)

    UCL = X̄ + 3MR

    LCL = X̄ – 3MR

  3. XbarR Chart

    UCL = X̄ + A2R

    LCL = X̄ – A2R

Where:

  • p is the sample proportion
  • n is the sample size
  • X̄ is the average of the sample means
  • MR is the average of the sample ranges
  • R is the range of the sample
  • A2 is a constant that depends on the sample size

Applications of Control Limits

  1. Process Monitoring

    Control limits are instrumental in monitoring process stability over time. They help identify points or patterns that fall outside the control limits, indicating the presence of special cause variation that requires investigation and corrective action.

  2. Process Improvement

    Control limits serve as a baseline for process improvement efforts. By understanding the natural variation within a process, organizations can focus on reducing special cause variation and bringing the process closer to its desired state.

  3. Predicting Process Behavior

    Control limits aid in predicting the expected range of variation in a process. This information is valuable for planning and decision-making, allowing organizations to anticipate and prepare for potential process deviations.

  4. Compliance and Certification

    Control limits are often used to demonstrate compliance with industry standards and regulations. They provide evidence of a well-controlled process, which is essential for certain certifications and accreditations.

Conclusion

Control limits are an essential element of control charts, enabling the distinction between common cause and special cause variation, providing a guide to process behavior, and facilitating process monitoring and improvement. By understanding the principles and applications of control limits, organizations can effectively manage and enhance their processes, leading to improved quality, efficiency, and customer satisfaction.

References

  1. https://www.isixsigma.com/dictionary/control-limits/
  2. https://www.qimacros.com/free-excel-tips/control-chart-limits/
  3. https://sixsigmastudyguide.com/control-chart/

FAQs

1. What are control limits?

Control limits are boundaries plotted on a control chart to distinguish between common cause variation and special cause variation in a process. They are typically set at +/- 3 standard deviations from the process average.

2. Why are control limits important?

Control limits help identify when a process is out of control, indicating the presence of special cause variation that requires investigation and corrective action. They also provide a guide to expected process behavior and facilitate process monitoring and improvement.

3. How are control limits calculated?

The calculation of control limits depends on the type of data being plotted on the control chart and the sample size. Common formulas include those for p charts, individual moving range (XmR) charts, and XbarR charts.

4. What is the purpose of setting control limits at +/- 3 standard deviations?

The choice of +/- 3 standard deviations is based on extensive research and experiments conducted by Walter Shewhart. This setting balances the probability of making two types of mistakes: calling common cause variation a special cause and calling special cause variation common cause.

5. Are control limits probability limits?

No, control limits are not probability limits. They are designed to work best at +/- 3 standard deviations and are not associated with any exact probability of detecting special cause variation.

6. What are the different types of control charts?

Common types of control charts include p charts for proportions, c charts for counts, u charts for defects per unit, np charts for nonconformities, XmR charts for individual measurements and moving ranges, XbarR charts for averages and ranges, and XbarS charts for averages and standard deviations.

7. How do control limits help in process improvement?

Control limits provide a baseline for process improvement efforts. By understanding the natural variation within a process and identifying special cause variation, organizations can focus on reducing defects and improving process performance.

8. Are control limits used for compliance and certification?

Yes, control limits are often used to demonstrate compliance with industry standards and regulations. They provide evidence of a well-controlled process, which is essential for certain certifications and accreditations.