Control Limits: Boundaries for Process Control

Control limits are statistical boundaries used in process control to determine whether a process variable is operating within an acceptable range.

In statistical process control (SPC), control limits are the thresholds used to determine whether a process variable (such as the mean or range) is in control or out of control. These limits are calculated from historical data and represent the boundary within which the process is considered to be stable and consistent.

Control limits should not be confused with specification limits, which are design constraints placed by customer requirements.

Types of Control Limits

Upper Control Limit (UCL)

The upper boundary of the control chart, above which a process is considered out of control.

Lower Control Limit (LCL)

The lower boundary of the control chart, below which a process is deemed out of control.

Center Line (CL)

The central value on the control chart, typically the mean of the process data.

Formulas

For a process with normally distributed data, control limits are commonly set at three standard deviations (σ) from the center line (mean, μ):

$$ \text{UCL} = \mu + 3\sigma $$

$$ \text{CL} = \mu $$

$$ \text{LCL} = \mu - 3\sigma $$

Special Considerations

Natural vs. Special Cause Variations

• Natural Cause Variation: Random and inherent variations in a process.
• Special Cause Variation: Non-random variations that indicate a malfunction or anomaly.

A process is “in control” if all data points fall within the control limits, and no patterns such as trends or cycles are present.

Historical Context

The concept of control limits was developed by Walter A. Shewhart in the 1920s at Bell Labs. Shewhart’s pioneering work laid the groundwork for modern quality control and process management techniques.

Applicability

Control limits are used across various industries like manufacturing, healthcare, and banking to ensure processes remain consistent and predictable.

Examples

Example of Calculating Control Limits

Suppose a manufacturing process has the following historical data:

• Mean (μ) = 100
• Standard Deviation (σ) = 5

The control limits would be:

$$ \text{UCL} = 100 + 3(5) = 115 $$

$$ \text{CL} = 100 $$

$$ \text{LCL} = 100 - 3(5) = 85 $$

This means any process data point above 115 or below 85 would be considered out of control.

Related Terms

• Control Chart: A graphical tool for monitoring process stability.
• Specification Limits: The range of acceptable values defined by customer requirements.
• Process Capability (Cp and Cpk): Metrics to measure how well a process can produce output within specification limits.

FAQs

What is the difference between control limits and specification limits?

Control limits are statistical boundaries based on process data, while specification limits are externally defined by customer requirements.

How often should control limits be recalculated?

Control limits should be recalculated whenever there is a significant change in the process or at regular intervals to ensure accurate monitoring.

What is an out-of-control process?

A process is out of control when data points fall outside the control limits or show non-random patterns, indicating special cause variation.

References

1. Montgomery, D. C. (2019). Introduction to Statistical Quality Control. Wiley.
2. Wheeler, D. J. (1999). Understanding Variation: The Key to Managing Chaos. SPC Press.
3. Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. D. Van Nostrand Company.

Summary

Control limits serve as vital statistical tools for monitoring the stability and consistency of a process. By comparing process data against these predetermined boundaries, organizations can ensure the quality and reliability of their operations, making control limits indispensable in fields that value precision and predictability.