Control charts separate normal process variation from signals that something has changed. Calculate control limits from subgroups or individual observations and flag out-of-control points and runs that deserve investigation.
How it works
Calculate control limits for an X̄-R chart from subgroups or an individuals and moving range (I-MR) chart from single observations, and flag points beyond the limits and runs on one side of the center line.
X̄-R: CL = X̿; UCL/LCL = X̿ ± A₂R̄; Range UCL = D₄R̄, LCL = D₃R̄
I-MR: CL = X̄; UCL/LCL = X̄ ± 2.66 × MR̄; MR UCL = 3.267 × MR̄
σ estimate = MR̄ ÷ 1.128 (d₂ for n = 2)Common uses
- Monitoring operational and financial KPIs over time
- Quality improvement and Lean Six Sigma projects
- Healthcare quality and patient-safety measures
Worked example
The calculator above opens with this example. Change any input to see the results update instantly, or select Reset to return to these figures.
| Chart type | X̄-R (subgroups) |
| Subgroups (one per line) | Week 1 | 32 35 31 34 33 Week 2 | 34 33 36 32 35 Week 3 | 31 34 33 35 32 Week 4 | 35 36 34 33 37 Week 5 | 33 32 34 31 35 Week 6 | 36 35 37 34 36 Week 7 | 34 33 35 36 33 Week 8 | 32 34 33 35 34 Week 9 | 38 41 39 40 42 Week 10 | 33 35 34 32 34 |
| Process status | Out of control |
| Center line (X̿) | 34.5 |
| Upper control limit | 36.5772 |
| Lower control limit | 32.4228 |
| Average range (R̄) | 3.6 |
| Subgroup size | 5 |
Investigate each signal for a special cause before recalculating limits; remove only points with an identified, corrected cause. Signals tested: points beyond the control limits, ranges beyond the range limit, and eight consecutive points on one side of the center line.
Interpreting the results
- Control limits describe what the process does, not what it should do; they are not specification limits.
- Base initial limits on 20 to 25 subgroups collected when the process is believed to be stable.
- Use I-MR charts for low-volume measures such as monthly cost per case or weekly days in A/R.
Frequently asked questions
What is the difference between control limits and specification limits?
Control limits are calculated from the process data and describe what the process actually does. Specification limits are set by customers or management and describe what the process should do. A process can be in control and still fail to meet specifications.
When should I use an I-MR chart instead of an X-bar R chart?
Use an individuals and moving range chart when each period produces a single value, such as monthly cost per case or weekly days in accounts receivable. Use an X-bar R chart when several measurements are taken in each subgroup.
What counts as an out-of-control signal?
Common signals include a point beyond a control limit and a run of eight or more consecutive points on one side of the center line. Each indicates a likely special cause that should be investigated.
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