1. What Are Control Limits?

Control limits, also known as natural process limits, are horizontal lines drawn on a statistical process control chart. They indicate the boundaries of common cause variation in a stable process.

2. How Control Limits Are Calculated

The calculator uses the standard control limits formula:

Where:

• \( \mu \) — Process mean
• \( \sigma \) — Process standard deviation
• UCL — Upper Control Limit
• LCL — Lower Control Limit

Explanation: The 3-sigma limits contain approximately 99.7% of the expected variation from a normally distributed process.

3. Importance of Control Limits

Details: Control limits help distinguish between common cause variation (inherent to the process) and special cause variation (due to external factors). Points outside these limits suggest the process may be out of control.

4. Using the Calculator

Tips: Enter the process mean and standard deviation. The calculator will compute the upper and lower 3-sigma control limits. Standard deviation must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: Why 3-sigma limits?
A: 3-sigma limits provide a balance between detecting important shifts while minimizing false alarms, covering 99.7% of normal variation.

Q2: When should control limits be recalculated?
A: After process improvements, when new data shows a different pattern, or when you have evidence the process has changed.

Q3: What if my data isn't normally distributed?
A: For non-normal distributions, consider transformations or alternative control chart methods like individuals charts with moving range.

Q4: Can control limits be used with attribute data?
A: Yes, but different formulas are used for p-charts (proportion) and c-charts (count) of defects.

Q5: What's the difference between control limits and specification limits?
A: Control limits reflect actual process performance, while specification limits are customer requirements. A process can be in control but not meet specifications.