I-MR Chart Calculator — Individuals and Moving Range
Paste a column of measurements and get the individuals and moving-range charts, with σ̂ from MR̄/d₂ or the median moving range, the run-rule set of your choice, and every constant named on the figure.
When an I-MR chart is the right chart
Use it when the rational subgroup is a single measurement — one reading per batch, per shift, per lot, per day. That covers most of chemical and process manufacturing, anything destructive to measure, and anything where the measurement is slow or expensive enough that you only take one.
If you can take three to five measurements close together under the same conditions, an X̄-R chart is a better instrument: subgrouping separates within-subgroup variation from between-subgroup variation, and the individuals chart cannot. The I-MR chart estimates short-term variation from consecutive differences instead, which works, and is more sensitive to the assumption that consecutive observations are comparable.
Data
Paste straight from Excel, Minitab or a CMM export — include the header row and the columns are matched by name, in any order.
| # | Sample(opt) | Measurement | New batch(opt) | |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 |
0 rows of data
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Enter data on the left to chart it
SVG is vector — it stays sharp at any size in a report. PNG 4× is roughly 600 dpi at figure width. Every export carries the estimator, the constants and the rule set drawn inside the figure, so the file is readable on its own.
Downloads carry a small “made with spcplot.com” credit along the bottom edge. The chart on screen is never watermarked, and the credit is a credit rather than a licence restriction — the figures are yours to publish either way. A Pro or Lifetime licence removes it.
Options
This plot has no adjustable options yet.
Your measurements are processed entirely in this browser tab. Nothing you type here is uploaded, so confidential production data stays confidential.
How the limits are computed
The moving range MRᵢ is |xᵢ − xᵢ₋₁|. Its average MR̄ estimates σ through the constant d₂ for a subgroup of the moving-range span: σ̂ = MR̄/d₂. The individuals limits are then x̄ ± 3σ̂.
You will more often see this written x̄ ± 2.66·MR̄. The two are the same statement: 2.66 is 3/d₂(2), rounded. This tool computes d₂ from the normal distribution rather than looking it up, so the factor it uses is 2.658681 — and the difference from 2.66 shows up in the fourth significant figure of the limit. That is small, and it is disclosed on the figure rather than hidden, because reproducing somebody else’s published number requires knowing which one they used.
The moving-range panel gets D₄·MR̄ as its upper limit and D₃·MR̄ as its lower. For a span of 2 D₃ is exactly zero, which is why the MR chart usually has no lower limit at all rather than one sitting on the axis.
Two things this tool will not do quietly
It will not choose your sigma estimator. The average moving range and the median moving range give different answers on the same data, and the difference matters when a single upset has inflated one range. Both are offered, neither is assumed, and the figure says which one produced the limits.
It will not compute a moving range across a batch boundary. Mark the first row of a new production campaign in the "New batch" column and the range that would have straddled the change is dropped instead of averaged in. A moving range across a campaign change measures the step between campaigns, not the short-term variation the chart is about — and left in, one such range can inflate σ̂ by a factor of ten.
Reading the figure
A solid line is the centre line; dashed lines are the control limits; a point drawn in red with a number beside it has failed the test with that number. The active rule set is printed under the chart, because Nelson, Western Electric and ISO 7870-2 flag different points on the same data — Nelson wants nine consecutive points on one side of the centre line, Western Electric eight, ISO seven.
The default is Nelson test 1 alone, which is what Minitab applies out of the box. Comparing this chart against an existing Minitab output should therefore agree point for point on the first try; switch to "Nelson, all 8" when you want the sensitivity and are willing to pay the false-alarm rate for it.
Common questions
- Why do my limits differ slightly from my textbook’s?
- Almost always the value of d₂. A table printing 1.128 and the exact 1.1283792 differ in the fourth significant figure of the limit. Set "Constant precision" to 3 dp to reproduce a published example exactly; the figure records which was used.
- How many points do I need before the limits mean anything?
- Shewhart’s guidance is at least 25. Below that the chart still draws, and it prints a warning saying how many points fed the limits — because limits from eight points will move as soon as a ninth arrives.
- Should I put my specification limits on this chart?
- No. Control limits describe what the process does; specification limits describe what the customer will accept. They answer different questions and putting them on the same axis is the classic way to conclude that an out-of-control process is fine because it is still inside spec. Capability analysis is where the two meet.
- Is my data uploaded anywhere?
- No. The whole calculation runs as JavaScript in this browser tab, and nothing on this site accepts a measurement — the only server code here takes a payment. That is why the tool is usable on data you are contractually barred from putting in a cloud service.