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Control limits calculator
Paste your data and get the center line, upper and lower control limits, a plotted chart and the points outside the limits. Not sure which chart? Use the control chart picker.
Formulas
| Chart | Center line | Control limits |
|---|---|---|
| I (individuals) | X̄ | X̄ ± 2.66 × MR̄ |
| MR (moving range) | MR̄ | UCL = 3.267 × MR̄, LCL = 0 |
| X̄ | X̿ | X̿ ± A₂ × R̄ |
| R | R̄ | UCL = D₄ × R̄, LCL = D₃ × R̄ |
| p | p̄ = total defective / total inspected | p̄ ± 3√(p̄(1 − p̄)/n) |
| np | np̄ | np̄ ± 3√(np̄(1 − p̄)) |
| c | c̄ | c̄ ± 3√c̄ |
| u | ū = total defects / total units | ū ± 3√(ū/n) |
2.66 = 3/d₂ and 3.267 = D₄ for a moving range of 2. A₂, D₃ and D₄ for every subgroup size are in the control chart constants table. A negative LCL is set to none.
Reading the chart
This calculator flags points beyond the 3σ limits (rule 1). Runs, trends and points hugging one side can also signal a special cause; see the Western Electric run rules. Limits computed from your own data are trial (Phase I) limits: find and fix the causes of any signals, then freeze the limits and use them for new data.
Read more: Choosing a control chart · I-MR chart · X̄-R vs X̄-S · Attribute control charts
FAQ
What is the difference between control limits and specification limits?
Control limits come from the process data and show what the process does when only common-cause variation is present. Specification limits come from the customer or the design and show what is acceptable. A process can be in control and still make parts out of spec; that is a capability problem.
How many data points do I need?
20 to 25 subgroups (or 20 to 25 individual values for an I-MR chart) is the usual minimum for trial limits. Fewer points give limits that move a lot when new data arrive.
Why is the lower control limit missing?
For counts and for ranges, a negative limit is impossible, so it is set to zero (no LCL). For p and u charts this happens when the average rate or the sample size is small.
Why are my p chart limits different for each point?
The limits depend on the sample size. When n changes from sample to sample, each point gets its own limits, which is why they look like steps.
Should I remove out-of-control points and recalculate?
Only after you find and remove the assignable cause. Then recalculate the limits without those points. If you cannot find a cause, keep the points in; dropping them makes the limits look tighter than the process really is.
This shows up on the exams as a calculation question. Practice it with new numbers every time, and every wrong answer explained.
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