1. What Are Control Limits?

Control limits are statistical boundaries used in process control and quality management to determine if a process is in a state of statistical control. They represent the expected variation in process output when only common causes of variation are present.

2. How To Calculate Control Limits

The standard formulas for 3-sigma control limits are:

Where:

• \( \bar{x} \) — Process mean (average)
• \( s \) — Standard deviation of the process
• \( UCL \) — Upper Control Limit
• \( LCL \) — Lower Control Limit

Explanation: The 3-sigma limits (±3 standard deviations from the mean) contain approximately 99.73% of normally distributed data, making them ideal for identifying special cause variation.

3. Importance of Control Limits

Details: Control limits help distinguish between common cause variation (inherent to the process) and special cause variation (due to specific circumstances). Points outside control limits indicate the process may be out of control and require investigation.

4. Using the Calculator

Tips: Enter the process mean and standard deviation. The calculator will compute both upper and lower control limits using the 3-sigma method.

5. Frequently Asked Questions (FAQ)

Q1: Why use 3-sigma limits instead of 2-sigma?
A: 3-sigma limits provide a higher confidence level (99.73% vs 95.45%) and reduce the chance of false alarms while still effectively detecting special causes.

Q2: When should control limits be recalculated?
A: Control limits should be recalculated when process improvements are made or when the process fundamentally changes to ensure they reflect current process capability.

Q3: What if my data isn't normally distributed?
A: For non-normal distributions, alternative methods like transformation or non-parametric control charts may be more appropriate than traditional 3-sigma limits.

Q4: How many data points are needed to calculate reliable control limits?
A: Typically, 20-30 subgroups or 100-125 individual measurements are recommended to establish reliable control limits.

Q5: Can control limits be used for attribute data?
A: Yes, different formulas exist for attribute data (p-charts, c-charts, u-charts) that account for the binomial or Poisson distribution of such data.