Free Control Chart Maker: Individuals (I-MR) Chart with 3-Sigma Limits

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One number per line, oldest first. You can paste a column from a spreadsheet; a header row is skipped. The sample below is example data.

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What is an I-MR chart?

An Individuals and Moving Range chart (I-MR, also called an X-mR chart) is the control chart for data that arrives one value at a time: one batch, one day, one invoice, one test result. The top chart plots each value against a center line (the average). The bottom chart plots the moving range, the absolute difference between each value and the one before it, which measures short-term, point-to-point variation.

How the limits are calculated

Center line = the average of your values (X̄).
Average moving range (MR̄) = the average of the differences between consecutive values.
Estimated sigma = MR̄ ÷ 1.128 (d₂ for ranges of two points).
Individuals limits = X̄ ± 3 × sigma, which is the same as X̄ ± 2.66 × MR̄.
Moving range upper limit = 3.267 × MR̄. Its lower limit is 0.

Sigma comes from the moving ranges, not from the overall standard deviation. That is deliberate: if the process shifted during the period, the overall standard deviation is inflated by the shift and the limits come out too wide to catch it.

Worked example (example data)

The sample above is made-up example data: 20 consecutive fill weights from a packaging line with a 50 g target. The average is about 50.13 g and the average moving range is about 0.44 g, which gives individuals limits of roughly 48.97 g to 51.29 g. Point 12 (51.6 g) is above the upper limit, so the chart flags it, and the moving range chart flags the jumps into and out of it (points 12 and 13). That is a signal to look for a special cause at that time, such as a nozzle change, a new material lot or a different operator, rather than to adjust the machine after every small wobble.

How to read it

Points inside the limits with no pattern: the process is showing only routine, common-cause variation. Adjusting it in response to single points usually makes things worse.
A point outside a limit: likely a special cause. Find out what was different at that time.
A spike on the moving range chart: a sudden jump between two consecutive values.
Control limits are not spec limits. Limits describe what the process does; specifications describe what the customer needs. A process can be in control and still make out-of-spec product. Checking that is a capability study (Cp, Cpk).

Common mistakes

Too few points. Aim for at least 20 to 25 values before trusting the limits; with fewer, treat them as provisional.
Out of time order. The moving range only means something when values are in the order they happened.
Recalculating limits every time. Once you have a stable baseline, keep those limits and judge new points against them. Recalculate only after a deliberate, confirmed change.
Using it for counts or proportions. Defect counts and percent defective have their own charts (c, u, p, np), which handle changing sample sizes properly.
Only checking points beyond 3 sigma. Runs and trends inside the limits can also be signals. This free tool flags only points beyond the limits; run rules such as Nelson or Western Electric catch more.

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Also free: the Pareto chart maker and the FMEA RPN calculator. See the template store for paid templates and apps.

Made by a Six Sigma Master Black Belt with 17 years of Lean Six Sigma process improvement experience.