KEVOS® MAKEOS · Quality
X-bar and R Control Chart Limits
What are the control limits for this X-bar and R chart?
Centre lines and upper and lower control limits for X-bar and range charts from the grand average, average range and subgroup size, with the estimated process standard deviation.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Grand average (average of subgroup means) | Average of the subgroup averages from at least 20–25 subgroups of a stable process. | |
| Average range | Average of the subgroup ranges. | |
| Subgroup size | choice | Number of measurements in each subgroup. |
Method and formulas
- X-bar limits = X̿ ± A₂ R̄.
- R limits: UCL = D₄ R̄, LCL = D₃ R̄.
- σ̂ = R̄ ÷ d₂. Constants for n = 2…10 (A₂, D₃, D₄, d₂) are the standard SPC values.
- Example: X̿ 25.01, R̄ 0.03, n = 5: X-bar limits 24.9927 to 25.0273; R UCL 0.06342.
Limitations
- Limits are valid only for a stable process; remove assignable causes before setting them.
- Control limits are not specification limits.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set up control charts for a process
- Recalculate limits after a process change
- Estimate process sigma for capability studies
Who it is for
- Quality engineers
- Process engineers
- Production supervisors
What you get
- X-bar chart centre line and limits
- R chart centre line and limits
- Estimated process standard deviation
Interpreting the result
- Points outside the limits, or non-random patterns, signal special causes to investigate.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
- ISO 7870-2 Control charts — Shewhart control charts
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