BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Grand average (average of subgroup means)
- What it is
- The average of all the subgroup averages from a stable process: the centre line of the X-bar chart.
- Units and format
- Enter a plain number with no unit. Negative values are accepted. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25.01 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same measurement unit as the ranges, and data from a period when the process was stable.
What this means: Average range
- What it is
- The average of the subgroup ranges, each range being the largest minus the smallest measurement in a subgroup.
- Units and format
- Enter a plain number with no unit. The form accepts 0 or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.03 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The control limits widen in direct proportion to the average range.
- Get it right
- Use the same unit as the grand average; it is not a standard deviation.
What this means: Subgroup size
- What it is
- The number of measurements in each subgroup, which selects the control chart constants.
- Units and format
- Choose one of 9 options from the list: 2; 3; 4; 5; 6; 7; 8; 9; 10.
- Example
- The form opens with “5” selected as a worked example. Choose the option that matches your case.
- Get it right
- All subgroups must be the same size for these limits to apply.
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
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Shewhart X̄ and R charts
In Control Charts by the Numbers
What it covers: Common and special causes, rational subgroups, X̄ and R limits from a stable baseline, where the constants come from, reading a day of SP-12's chart, and why tolerance limits do not belong on it.
Method explained here · Library collection
Statistical process control on the shop floor: control charts, real signals and when to leave a process alone
What it covers: Control charts separate the normal noise of a process from real change. How to choose a chart, set limits, read the signals and stop well-meant adjustments that make variation worse.
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