A Shewhart chart is a control chart. The two terms mean the same thing, and the first is simply the proper name — after Walter A. Shewhart, who invented the device at Bell Telephone Laboratories and described it in a one-page memorandum dated 16 May 1924.
That memo contained a diagram that is recognisably every control chart drawn since: a running plot of a measured quantity, a centre line, and a pair of limits computed from the data rather than chosen by anyone.
The idea that was new
Statistics before Shewhart largely concerned itself with fixed populations — sample from a pot, infer the pot. Shewhart was looking at a production process, which is not a pot. It is a thing running over time that may or may not be the same thing tomorrow.
His insight was to split variation in two, and to make the split operational:
- Common cause — the many small influences always present. The process being itself.
- Special cause (he called it assignable cause) — something identifiable that is not normally there.
The chart's purpose is to tell them apart with a known error rate, because the correct response to each is opposite: investigate a special cause, leave common cause alone. Acting on common cause as though it were a signal makes the process measurably worse — there is a fuller guide on that distinction, and it is the reason the chart exists at all.
Why three sigma
The single most asked question about the chart, and the answer disappoints people who expect a derivation.
Three sigma is an economic choice, not a statistical one. Shewhart said so explicitly. He was balancing two costs:
- Limits too narrow → frequent false alarms → people chase problems that are not there → within a month nobody believes the chart.
- Limits too wide → real signals slip through → the chart certifies a process that is misbehaving.
Three sigma sat, in his experience and everyone's since, at the point where the chart is worth looking at. It corresponds to roughly one false alarm in 370 points if the underlying data is normal — but the justification never depended on normality, and Shewhart was careful about that. The chart works on skewed data too, which is why it survived contact with real factories.
Note what three sigma is not: it is not the specification, it has nothing to do with what the customer will accept, and "3σ" here is unrelated to the sigma levels in Six Sigma programme naming. Control limits come from the process. Specification limits come from the drawing. They answer different questions and, on a subgrouped chart, they must not share an axis.
The family, and how to choose
"Shewhart chart" covers a family. Which one you need is decided by what you are measuring and how it arrives.
Measured values (variables data)
| Chart | Use it when | Sigma from |
|---|---|---|
| I-MR | One reading at a time — a batch, an oven, a destructive test | Mean moving range / d₂ |
| X̄-R | Subgroups of about 2–9 parts | R̄ / d₂ |
| X̄-s | Subgroups of about 9 or more | s̄ / c₄ |
Subgroup where you can. Averages of five readings vary √5 less than the readings themselves, so an X̄ chart notices a shift in the centre far sooner than an individuals chart ever will. I-MR is for when the process refuses to give you subgroups, not for when subgrouping feels like effort.
Counted values (attributes data)
| Chart | Counts | Sample size |
|---|---|---|
| p | Proportion defective | May vary |
| np | Number defective | Constant |
| c | Defects per unit | Constant |
| u | Defects per unit | May vary |
If you can measure rather than count, measure. A measurement carries far more information per part, and an attributes chart needs very large samples to detect anything.
Charts that are not Shewhart charts
EWMA and CUSUM weight past observations instead of judging each point independently. They detect small sustained shifts much faster than a Shewhart chart does, at the cost of being slower on large sudden ones and much harder to explain on a shop floor. They are the right tool for a slow drift you already know you are hunting.
The run rules
A point can sit inside the limits and still be telling you something. Shewhart noted this; the Western Electric handbook of 1956 codified it; Lloyd Nelson published the version most software uses in 1984.
The four that are safe on almost any data:
- Beyond 3σ — one point past a control limit.
- Shift — nine in a row on the same side of the centre line.
- Trend — six in a row rising, or six falling.
- Alternating — fourteen in a row zig-zagging.
The zone rules (Nelson 5 to 8) count points in the one-sigma and two-sigma bands. They are more sensitive, and they assume the data is roughly normal and that consecutive readings are independent — assumptions a pasted sample cannot be presumed to meet. Switch them on knowingly, per characteristic, not by default.
Every rule you enable adds false alarms. Run all eight and the false-alarm rate roughly quadruples. More rules is not more rigour.
What a hundred years has not changed
The 1924 memo would still pass review. What has changed is only where the chart lives: it moved off the paper on the machine, into a spreadsheet, and — where the limits need to stay still and someone needs telling when a rule trips — off the spreadsheet again.
Shewhart's actual requirement was never the arithmetic. It was that the chart be in front of the person who can act on it, soon enough for the action to matter.