SPC Control Chart

What this tool does

CM8-209 draws the two charts statistical process control is built on: an X̄ chart of subgroup means and an R chart of subgroup ranges, with centre lines and control limits calculated from your own measurements using the standard A₂, D₃, D₄ and d₂ constants. It marks points beyond a limit, finds runs of seven on one side of the centre line, and estimates the process sigma from R̄.

You record one row per subgroup: a small sample of consecutive parts taken at one moment. Everything runs inside this file — no account, no upload, no network request of any kind.

Common cause, special cause and tampering

Every process varies, and SPC rests on separating two kinds of variation. Common cause is the background noise of a process running as designed — material, temperature, clamping, the gauge — which nobody caused today and which only a change to the process reduces. Special cause was not there before: a tool wearing out, a coolant failure, a wrong setting. It has a findable cause and can be removed.

A control chart tells the two apart, and most of its value lies in what it stops you doing. When an operator adjusts a machine because the last part measured slightly high, and it was high only through ordinary noise, the adjustment corrects nothing — it adds an offset to variation that was going to average out anyway. The next part is then low, inviting the opposite adjustment. This is tampering, and it is no small inefficiency: reacting to noise as though it were a signal reliably makes output more variable than leaving the process alone. Deming's funnel experiment showed it with a marble; every factory shows it daily with a well-meaning operator. Hence the discipline: inside the limits with no rule fired, do nothing — and when a rule does fire, go and look while the evidence is still on the machine.

Subgroups, and how to take them

A subgroup is a small sample — usually three to five consecutive parts — measured at one point in time. One row per subgroup, not one per part, because both charts come from the mean and the range within each subgroup. That carries the assumption everything depends on, and it has a name: rational subgrouping. Take the sample so the variation inside a subgroup is only common cause and any special cause appears between subgroups: consecutive parts, one machine, one operator, one tool, close together in time.

The classic mistake is a subgroup built from one part off each of four machines. The within-subgroup range then contains the machine-to-machine differences, inflating R̄, widening the limits, producing a chart that can never signal anything. Four machines are four processes and want four registers; likewise mixed shifts, cavities or part numbers.

Read the R chart first

This is the reading order people get backwards. The limits on the mean chart are derived from R̄: the average within-subgroup range estimates the spread, and A₂R̄ is how far the limits sit from the centre line. If the range chart is out of control, R̄ averages two or more different states and the limits on the mean chart are arithmetic without meaning.

So look at the R chart first. If it is stable, the mean chart can be interpreted. If it is not, find out why the spread is moving — a loose fixture, a worn bearing, two operators using the gauge differently — before reading anything into the mean.

The formulae and the constants

• n — A₂ — D₃ — D₄ — d₂
• 2 — 1.880 — 0 — 3.267 — 1.128
• 3 — 1.023 — 0 — 2.574 — 1.693
• 4 — 0.729 — 0 — 2.282 — 2.059
• 5 — 0.577 — 0 — 2.114 — 2.326

D₃ is zero at these sizes, which is why the lower range limit is zero: with a small sample no range is small enough to be evidence of anything. The constants encode the three-sigma distance for the mean of n readings, so the limits sit three standard errors from the centre — not three standard deviations of individual parts.

Control limits are not specification limits

This is the commonest confusion in SPC and it is worth being blunt about. Control limits come from the process. Specification limits come from the customer. They mean different things and must never share a chart.

A control limit states what this process does: given the variation it has, a subgroup mean falls inside these lines unless something changes. Nobody chose the number; it falls out of the measurements. A specification limit states what somebody will accept, and would be identical had you never measured.

So both surprising combinations are possible. A process can be in perfect statistical control and entirely outside specification: stable, predictable, predictably making scrap. The charts show nothing wrong because nothing is changing; the process is in the wrong place or too variable, and the answer is to re-centre it or reduce its variation, not to hunt a special cause. Equally a process can sit inside specification while wildly out of control, the tolerance hiding the instability. Putting specification limits on a control chart is therefore harmful: it invites adjustment whenever a point drifts toward a tolerance, which is tampering with extra steps. This tool draws them on the distribution chart, and nowhere else.

The rules this tool applies

Two of the Western Electric rules are implemented, and the tool marks where each fires:

• Rule 1 — a point beyond a control limit. Any subgroup mean above the UCL or below the LCL, or any range above the upper range limit — the strongest single signal there is.
• Rule 2 — seven or more consecutive points on one side of the centre line. No point need be near a limit. A run says the process has shifted to a new level, and it often fires before anything crosses a limit.

That is a subset, labelled honestly. The full set adds rules on the outer zones of the band, on trends, on alternation and on hugging the centre; those need the chart divided into sigma zones, and every rule added raises the false-alarm rate as well as the sensitivity.

Special causes and honest exclusion

When a signal is investigated and a genuine special cause is found and removed, that subgroup no longer represents the process, and leaving it in inflates R̄ and widens the limits. Tick known special cause, write what it was, and the subgroup is left out of X̿, R̄, both sets of limits and the run rules while staying visible in the register.

Exclude only when all three hold: the cause is known, it is genuinely not part of the normal process, and it has been removed. A point you dislike is not a special cause; nor is an unexplained one. Dropping points because they spoil the picture turns a control chart into advocacy, and the tool will not accept an exclusion with nothing written against it.

How many subgroups before you trust the limits

The usual guidance is 20 to 25 subgroups, because R̄ is itself an estimate: from a handful it is imprecise, and imprecise limits either miss signals or invent them.

Twelve is a start — enough to see the shape of the process — and that is what the sample data holds. Treat such limits as provisional, say so on anything you circulate, and recalculate at twenty-five. After that, recalculate when the process is deliberately changed and once a special cause has been removed. Never recalculate because a point went outside: widening limits until the data fits is the opposite of process control.

What this tool does not do

It does not calculate capability. Cp and Cpk compare the process spread with the specification and are meaningless until these charts show a stable process — an index computed on an unstable one describes something that will not be true next week. Establish control here, then take the estimated sigma and the specification limits to the Process Capability tool.

The spreadsheet workflow

• Spreadsheet template in the toolbar saves a CSV whose headings are exactly this tool's column names — characteristic measured, process or machine, subgroup number, sample date, Measurement 1 to Measurement 5, unit of measurement, operator, notes and the two special-cause columns — with a guidance row showing what each expects.
• Fill in one row per subgroup, each reading in its own Measurement column, then delete the guidance row and save as CSV.
• Import spreadsheet reads it back, matching columns by heading, so order does not matter and extra columns are ignored. Rows failing a check are skipped and reported by row number.

Nothing is uploaded: the file is read by this page. If your spreadsheet holds one part per row, reshape it into subgroups first — that reshaping is the subgrouping decision, so make it deliberately.

FAQ

A point went out but every part was in tolerance. Do I care? Yes. The chart is telling you the process changed, and finding out now is cheaper than at the next signal.

Why do the limits not move when I filter the register? Limits are a property of the process, not of the view. Filtering changes which points are drawn; the centre lines, limits and rules always come from every subgroup that is not excluded.

Can I chart pass/fail data here? No — X̄ and R charts are for variable data, measured on a continuous scale. Counts need attribute charts.

Saving your work

Subgroups, settings and the report header are written to this browser's local storage as you type — one browser on one computer, so a private window or a tool that clears site data will not have them.

Treat Export .json as the real save — one file containing everything, which Import .json restores anywhere. Export CSV gives every filtered subgroup with its mean and range. Reset asks twice, then erases everything.

Accuracy & disclaimer

The arithmetic is elementary and performed faithfully. Everything deciding whether the answer is true sits underneath it: rational subgrouping, a gauge that can resolve the variation, readings recorded in the order taken, and honest exclusions.

Limits from twelve subgroups are provisional. Recalculate at twenty to twenty-five, and never because a point went out. This is a calculation and record-keeping aid, not a quality management system, and not advice on whether a part is fit to ship.