Individuals & Moving Range Chart

What this tool does

CM8-357 draws an individuals and moving range chart — the control chart for processes where you get one measurement at a time rather than a subgroup of five. It calculates the centre line and control limits from your own data, applies four run rules, shows how far each reading sits from the centre in sigma, and works out capability against your specification.

Everything runs inside this single file — no account, no upload, no network request of any kind.

When an I-MR chart is the right chart

Use it when the natural sample size is one:

• Destructive or expensive testing, where you measure one piece and no more.
• Batch processes — one viscosity, one pH, one yield per batch.
• Slow processes where five consecutive pieces would take a week.
• Administrative measures — one figure per day, per week, per month.

Where you genuinely take subgroups of four or five, an X-bar and R chart is more sensitive and you should use that instead. An I-MR chart is the honest option when subgrouping would be a fiction.

Order is everything

A control chart is a chart of a process over time. Readings are analysed in date order, then by the sequence number within the day, so several readings on the same date keep the order you took them in.

Sorting the data any other way — by value, by part number, by operator — destroys the chart. The moving range is the difference between consecutive readings, so if the order is wrong, every limit on the page is wrong. This is the single easiest way to produce a control chart that looks convincing and means nothing.

How the limits are calculated

Note what is not in there: the standard deviation of all the readings. Using that would build the limits from the same variation you are trying to detect, and a process that drifts would produce limits wide enough to contain its own drift. The moving range uses only the difference between neighbours, which captures short-term variation and nothing else. That distinction is the whole idea behind a control chart.

Where 2.66, 1.128 and 3.267 come from

They are not arbitrary. For a moving range of two consecutive values, the expected range of a normal distribution is 1.128 standard deviations — that constant is d₂. So sigma is estimated as MR bar ÷ 1.128, and three sigma is 3 ÷ 1.128 = 2.66 times MR bar. The moving range limit constant 3.267 is the equivalent for the range itself. All three are for a moving range of two; if you ever see different figures quoted, they are for a different subgroup size.

How many readings you need

Two thresholds, both of which you can set:

• Below the minimum (10 by default) no limits are drawn at all. The chart plots the readings and says so. Limits calculated from six points are numerology.
• Between the minimum and the firm threshold (25 by default) limits are drawn and labelled provisional, on the chart and in the calculation table. Use them, watch them, and expect them to move.
• At or above the firm threshold the limits are treated as established.

Twenty to twenty-five readings is the conventional minimum for stable limits, and it is a convention worth keeping. The sample data has twelve readings on purpose, so you can see what provisional limits look like.

Once limits are firm, stop recalculating them every time you add a point. Fix them, and judge new readings against the fixed limits. A chart whose limits move with every reading can never show you that the process has shifted, because the limits shift with it.

Read the moving range chart first

This is the habit that separates people who use control charts from people who produce them. The individuals limits are calculated from the moving range, so if the moving range chart is out of control, the limits above it are built on a broken estimate and nothing on the individuals chart can be trusted.

A single spike on the moving range chart usually means one reading is odd. A moving range chart that is out of control in several places usually means the process variation itself is unstable, and the answer is not a tighter tolerance — it is finding out why.

The four run rules

A point outside the limits is the obvious signal. The others catch a process that has shifted without any single reading being extreme:

• Rule 1 — one reading outside the control limits, or one moving range above its upper limit.
• Rule 2 — nine readings in a row on the same side of the centre line. A shift.
• Rule 3 — six in a row steadily rising or falling. A trend: tool wear, a bath depleting, a filter loading up.
• Rule 4 — fourteen in a row alternating up and down. Usually two alternating sources — two heads, two operators, two fixtures — being charted as one.

These are the four that apply cleanly to individuals data. Longer rule sets exist that use the zones between one and two sigma, and they are more sensitive to small shifts but also produce more false alarms on an I-MR chart, where the underlying distribution is less well behaved than for subgroup means. Four rules is a defensible choice; if your organisation mandates a different set, apply them by eye using the sigma column.

Every rule carries a false-alarm rate. On a stable process, roughly one point in three hundred will fall outside the limits by chance. A single signal is a prompt to go and look, not proof that something has changed.

Excluding a reading

Ticking exclude removes a reading from the limit calculation while still plotting it, drawn in amber. The tool will not accept an exclusion without a reason, and that is deliberate.

The only defensible grounds for excluding a point are that you know what caused it and the cause has gone: a loose clamp found and tightened, the wrong material traced and quarantined, a measurement taken with a gauge later found out of calibration. Write the investigation in the note.

Excluding points because they widen the limits is how a control chart becomes decoration. If you find yourself excluding several, the honest conclusion is usually that the process is not in control and the limits should not be fixed yet.

What happens to the moving ranges either side. An excluded reading sits between two others, so two moving ranges touch it — and both are enormous, because that is why you excluded it. If those ranges stayed in the calculation, the reading you removed would come straight back in through the estimate of variation and roughly double the limits, which is the opposite of what excluding it was for. So the limits are calculated from the series with the excluded readings taken out and the gap closed: the moving range bridges from the last included reading to the next one. The moving range chart still plots the real jumps, in red, because they are what happened.

Control limits are not specification limits

This is the misunderstanding that costs the most, so it is worth being blunt about.

Control limits come from the process. They say what this process does when nothing unusual is happening. Specification limits come from the customer or the drawing. They say what is acceptable. Neither has any influence on the other.

The individuals chart here deliberately does not draw specification limits, because a chart showing both invites the two most common errors in the field: adjusting a process because a reading approached a specification limit while remaining perfectly in control, and relaxing about a process drifting steadily upward because it is "still in tolerance". A process can be in perfect control and produce scrap continuously; it can also be wildly out of control and inside specification all week.

Specification limits are used in exactly one place in this tool — the capability figures — which is where they belong.

Cp and Cpk

Cp asks whether the process is narrow enough to fit inside the specification. Cpk asks whether it is narrow enough and centred. A high Cp with a low Cpk is a capable process pointing at the wrong place — usually the cheapest quality problem there is to fix, because it needs an adjustment rather than an improvement.

The common thresholds are 1.33 as a working minimum and 1.67 where the consequence of a defect is serious. They are conventions, not laws, and customers set their own.

Capability means nothing on a process that is not in control. The sigma in both formulas is an estimate of stable, short-term variation. If the moving range chart shows the variation itself is unstable, the estimate is not describing anything that will still be true next week, and the capability figures are arithmetic rather than information. The tool calculates them whenever both specification limits exist; deciding whether they mean anything is your job.

Assumptions that can break this chart

• One stream. Readings from three machines pooled onto one chart produce limits that describe none of them. The machine chart exists to make that visible.
• No autocorrelation. If each reading is strongly related to the one before — a tank temperature sampled every minute, a level that drains slowly — the moving ranges are artificially small and the limits come out far too narrow, so the chart cries wolf constantly.
• Roughly symmetric data. I-MR charts tolerate mild non-normality well, but for strongly skewed data such as impurities near zero or times to failure, the lower limit in particular can be meaningless or negative.
• Measurement that can see the variation. If your gauge resolution is coarse relative to the process spread, the moving ranges collapse to a few discrete values and the limits are an artefact of the gauge. A quick check: if fewer than five distinct values appear across your readings, resolve the measurement before trusting the chart.

Printing and sharing

The Report tab prints both charts, the calculation table and the signals table with a title block you fill in. The calculation table is the one to keep: it shows every constant and every step, so an auditor or a customer can reproduce your limits by hand.

Saving your work

Readings are held in this browser, on this computer, and stay there between visits. Use the backup button to write a JSON file you control; the spreadsheet download gives you the same readings with their moving ranges.

Accuracy & disclaimer

The constants and formulas are stated in full above so any figure here can be checked by hand. What the tool cannot check is whether your readings came from one process, were taken in the order you say, or were measured with a gauge capable of the job. A control chart built on any of those being untrue will still look entirely convincing.