How this calculator works
Control limits surround a process centre by a selected number of standard deviations of the monitored statistic. Mean charts use σ/sqrt(n), p charts use sqrt(p(1-p)/n), and c charts use sqrt(c). Proportion limits are clipped to [0,1] and count lower limits to zero. Use a stable baseline and constant sample size or exposure. The table flags only values beyond limits; it does not implement run rules.
Formula
UCL = centre+k SD(statistic); LCL = centre-k SD(statistic). X̄ chart SD = σ/√n; p chart SD = √(p(1-p)/n); c chart SD = √c.
Worked example
For individual measurements with mean 100 and process SD 5, three-SD limits are 85 and 115. For means of 25 such observations, they narrow to 97 and 103.
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Frequently asked questions
Are control limits specification limits?
No. Control limits describe process behaviour; specifications describe an external requirement.
Can I estimate SD from moving ranges here?
This tool requires the process SD directly. It does not estimate moving-range or subgroup-range constants.
Do points inside the limits guarantee control?
No. Trends, runs, changing variance and dependence can still indicate process changes.