Control Chart Limits Calculator
Upper and lower control and warning limits for a control chart, from the process mean and standard deviation.
Results
Upper control limit
51.2000
Lower control limit
48.8000
Upper warning limit
50.8000
Lower warning limit
49.2000
Total band width
2.4000
What this tool does
Control limits describe what the process normally does, not what the drawing asks for — they come from the data itself. A point outside them is a signal that something has changed and is worth chasing; points inside are just the process being itself, and reacting to them makes things worse.
Formula
UCL = X̄ + 3σ , LCL = X̄ − 3σ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
mn | Mean (average) | — |
sd | Standard deviation (sample) | — |
k | Sigma multiple | — |
UC | Upper control limit | — |
LC | Lower control limit | — |
UW | Upper warning limit | — |
LW | Lower warning limit | — |
BW | Total band width | — |
Worked example
- Mean (average)50
- Standard deviation (sample)0.4
- Sigma multiple3
- Upper control limit51.2000
- Lower control limit48.8000
- Upper warning limit50.8000
- Lower warning limit49.2000
- Total band width2.4000
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
Why three sigma and not two?
Because at two sigma, roughly one point in twenty falls outside the limits by pure chance, and a chart that cries wolf every twenty samples gets ignored. At three sigma that drops to about three points in a thousand, so a point outside is worth investigating. The two-sigma lines are still useful as warning limits.