Quality & Six Sigma

Control Limits Calculator

Paste your process data and instantly see UCL, CL, and LCL — with a live control chart that flags out-of-control points and Western Electric rule violations.

I-MR formulas
CL  = x̄
UCL = x̄ + 3(MR̄/d₂)
LCL = x̄ − 3(MR̄/d₂)
UCLMR = D₄ · MR̄

Enter your data

Paste numeric values separated by commas, spaces, or new lines. Minimum 5 data points required.

2–10 per subgroup Subgroup size must be between 2 and 10.
Paste values separated by commas, spaces, tabs, or new lines Enter at least 5 valid numeric values.
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Ready to calculate

Choose your chart type, paste your data, and press Calculate to see control limits and a live chart.

Individuals Chart (X) — Control Limits
UCL
Upper control limit
CL
Centre line (mean)
LCL
Lower control limit
Moving Range Chart (MR) — Control Limits
UCLMR
Upper control limit
CLMR
Centre line (MR̄ or R̄)
LCLMR
Lower control limit
n points
Mean
Out-of-control
Std dev (s)
Out-of-control points (X chart)
What this means

Individuals Chart (X)
Each point is one measurement. Red points are outside the 3σ control limits.
UCL / LCL
Centre line
Out-of-control
Moving Range Chart (MR)
Absolute difference between consecutive measurements. Points above UCL indicate unusual spikes.
UCL
MR̄
How to Respond to Your Chart
Practical actions based on what your control chart is showing
How it works

Understanding control charts

Control limits are not spec limits

UCL and LCL are calculated from the data itself — they represent natural process variation (±3σ). A point outside the limits signals an unusual event, not necessarily a defect. Spec limits are set by the customer; control limits are set by the process.

I-MR

When to use each chart type

Use I-MR when you measure one item at a time or data is collected infrequently — one reading per time period. Use X̄-R when you sample groups of 2–10 items at regular intervals and want to detect both mean shifts and variation changes.

WE

Western Electric rules

Beyond single out-of-control points, Western Electric rules flag non-random patterns: 8 consecutive points on one side of the centre line, 6 points in a trend, or 2 of 3 points in the outer third of the chart — all indicate process changes worth investigating.