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Upper Control Limit Calculator — result sheet
Calculate center, upper, and lower three-sigma-style limits for a sample-mean control chart.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a mean chart, UCL=μ+kσ/√n; center=μ; LCL=μ−kσ/√n.
The subgroup-size term makes the limit narrower for averages than for individual observations, while the multiplier remains an explicit planning choice.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Process mean — minimum -1000000000000; maximum 1000000000000
- Process standard deviation — minimum 1.0E-6; maximum 1000000000000
- Subgroup size — minimum 1; maximum 1000000
- Sigma multiplier — minimum 1.0E-6; maximum 100
Worked example
| Input | Value |
|---|---|
| Process mean | 100 |
| Process standard deviation | 4 |
| Subgroup size | 5 |
| Sigma multiplier | 3 |
Center = 100; UCL ≈ 105.367; LCL ≈ 94.633.
Assumptions and limits
- The standard deviation describes the in-control process and is compatible with the subgroup mean.
- The limits are a planning calculation, not proof that a process is stable.
- Autocorrelation, estimated control-chart constants, phase-I selection, and special-cause rules are not modeled.
- A lower limit can be mathematically valid even when a real-world characteristic has a natural floor.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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