X-Bar Control Chart Limits Calculator
Calculate three-sigma upper and lower control limits for an X-bar chart from a process mean, within-process standard deviation and subgroup size.
How to use this calculator
- Enter mean, positive process standard deviation and subgroup size.
- Confirm that all inputs use the stated units and the same population, period or scope.
- Change one assumption at a time when comparing scenarios.
Formula used by the control chart limits calculator
UCL/LCL = mean ± 3σ/√n
- UCL/LCL = mean ± 3σ/√n
- This is the basic X-bar limit equation; production chart selection may require control constants or an R/S chart.
- Inputs are validated against required ranges and outputs are rounded for readability.
Worked examples
Worked example
Mean 25, standard deviation 2 and subgroup size 5.
The limits are centred on 25 with a half-width of 3×2/√5.
The limits are centred on 25 with a half-width of 3×2/√5.
Understanding the result
Calculate three-sigma upper and lower control limits for an X-bar chart from a process mean, within-process standard deviation and subgroup size.
This is the basic X-bar limit equation; production chart selection may require control constants or an R/S chart.
Important notes
This is the basic X-bar limit equation; production chart selection may require control constants or an R/S chart.
Use the result as a calculation aid for the inputs supplied; confirm critical specifications independently.
Frequently asked questions
Are control limits specification limits?
No. Control limits describe process variation; specification limits describe requirements.
Does a point outside limits prove the cause?
No; it signals a potential special cause to investigate.
How do I use this calculator?
Enter mean, positive process standard deviation and subgroup size.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.