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What is an SPC chart?

Last reviewed 2026-08-21

An SPC chart — statistical process control chart, also called a control chart or a Shewhart chart — is a plot of measurements in the order they were produced, with a centre line and two limits drawn across it.

The limits are the whole point, and they are the thing most people get wrong.

The one distinction that matters

Control limits come from the process. Specification limits come from the customer. They are not the same numbers and they never go on the same chart for the same purpose.

  • Specification limits are what the part is allowed to be. A drawing says 10.00 ± 0.05 mm, so USL is 10.05 and LSL is 9.95. Somebody decided that.
  • Control limits are what the process is actually doing. They are calculated from the measurements themselves — typically the centre line plus and minus three standard deviations, estimated from within-subgroup variation. Nobody decides them; they are measured.

Putting spec limits on a control chart and calling the result an SPC chart is the single most common mistake in the field. The chart then answers "are we making scrap?" — which you already knew — instead of "has something changed?", which is the question only a control chart can answer.

A process can sit comfortably inside specification while its control chart screams that a tool is wearing. That signal arrives days before the first bad part. That is the value, and you throw it away by drawing the wrong lines.

What the chart is actually testing

Every process varies. Shewhart's insight was that variation comes in two kinds:

  • Common cause — the ordinary background noise of a process that is behaving as itself. Many small influences, none dominant. Predictable within limits.
  • Special cause — something that was not there before. A new material lot, a fresh operator, a tool that has worn past a threshold, a machine that was bumped.

The control limits mark the boundary of what common cause alone can plausibly produce. A point outside them is evidence that something changed. That is a statistical test, run continuously, on every part you measure — which is why the chart is worth having and a table of numbers is not.

Full treatment in common cause and special cause variation.

Which SPC chart to use

The chart type follows the data type. Get this wrong and the limits are wrong.

Measurements — length, weight, temperature, pressure (variables data):

Chart Use when Limits from
X̄-R Subgroups of 2–9 consecutive parts Subgroup means and ranges (R̄/d₂)
X̄-s Subgroups of 10 or more Subgroup means and standard deviations (s̄/c₄)
I-MR One reading at a time — batch processes, slow production, destructive tests Individuals and the moving range between consecutive readings

Counts — defects and defectives (attributes data):

Chart Plots Use when
p Proportion defective Sample size varies
np Number of defective units Sample size is constant
c Number of defects Constant area of opportunity
u Defects per unit Area of opportunity varies

The count charts trip people up because defect and defective are different things. A unit is defective or it is not — one per unit, maximum. A unit can carry several defects: three scratches on one panel is one defective unit and three defects.

So: the chart that plots the number of defects is the c chart, when every sample covers the same area of opportunity — the same panel size, the same length of weld, the same hour of running. When that area changes between samples, use the u chart, which divides by it. If you are counting whole units that passed or failed rather than flaws on them, you want p or np instead.

How to read one

A point outside the control limits is the obvious signal, and it is not the only one. Runs of points inside the limits can be just as improbable, and they arrive earlier:

  • Nine in a row on one side of the centre line — the process has shifted.
  • Six in a row rising, or six falling — a trend. Tool wear, a bath depleting, something warming up.
  • Fourteen alternating up and down — usually two things being sampled as one: two spindles, two heads, two shifts.
  • Two of three points beyond 2 sigma on the same side — a shift too small for a single point to catch.

These are the Nelson and Western Electric rules, and each pattern has a characteristic cause worth knowing. The rules checker evaluates all of them on pasted data and names what each violation usually indicates.

One warning about run rules: every rule you add raises the false-alarm rate. A chart running eight rules trips on a stable process more often than a chart running one. Pick the rules that match the failures your process actually has.

A worked example

Five parts measured every hour, ten hours, target 10.00 mm:

Hour  Readings                              X̄       R
 1    10.02 9.99 10.01 10.00 9.98         10.000   0.04
 2    9.99 10.01 10.00 10.02 9.99         10.002   0.03
 3    10.01 10.00 9.98 10.01 10.00        10.000   0.03
 4    10.00 10.02 10.01 9.99 10.01        10.006   0.03
 5    9.98 10.00 9.99 10.01 10.00          9.996   0.03
 6    10.03 10.04 10.02 10.05 10.03       10.034   0.03
 7    10.04 10.05 10.03 10.04 10.06       10.044   0.03
 8    10.05 10.06 10.04 10.07 10.05       10.054   0.03
 9    10.06 10.05 10.07 10.06 10.08       10.064   0.03
10    10.07 10.08 10.06 10.09 10.07       10.074   0.03

R̄ ≈ 0.031, and for subgroups of five A₂ = 0.577, so the X̄ chart limits sit about ±0.018 around the grand mean.

Every single reading is inside a ±0.05 tolerance. A spec-limit chart shows ten hours of good parts and says nothing. The control chart shows five hours flat, then a steady climb — five consecutive rising subgroups, drifting past the upper control limit at hour 8. That is tool wear, and it is visible around hour 7, comfortably before the first part goes out of tolerance around hour 12.

The chart bought five hours of warning. That is what an SPC chart is for.

SPC charts in Excel

Excel will draw one. Plot the values as a line chart, add three more series holding the centre line and the two limits, and format them flat. The arithmetic is a handful of AVERAGE and STDEV.S calls plus the d₂ or A₂ constant for your subgroup size.

It works, and it has three failure modes worth knowing before you commit a quality system to it:

  1. The limits move when data is added. If the limit cells reference the whole column, every new reading recalculates the limits — so a drifting process quietly drags its own limits along behind it and never signals. Control limits are supposed to be frozen from a baseline period.
  2. Nothing checks the chart. A run rule only trips if a person is looking at the chart at the moment it trips.
  3. The workbook belongs to whoever built it. Which is fine until they leave.

Point 1 is the serious one, because a spreadsheet with sliding limits looks exactly like a working control chart right up until the day you needed it to signal. SPC charts without Excel covers what to do about all three.

Try it on your data

Free, no signup, nothing stored.

Run these on your own numbers

Free, no signup, and nothing you paste is stored — the same tested engine that draws the charts in the product, so the answers cannot disagree.

  • Control chart generator — Paste a column of numbers, or rows of subgroups, and get a real control chart: limits from the data, Nelson rules 1–4 evaluated, out-of-control points marked.
  • Nelson & Western Electric rules checker — Every run rule evaluated on your data, each violation named in plain English with what it usually indicates — a shift, a trend, tool wear, two machines mixed.
  • X̄-R chart calculator — Subgroups in, X̄ and R charts out — limits from A₂, D₃ and D₄, run rules evaluated, and the range chart shown first because it decides whether the averages chart can be trusted.
  • I-MR chart calculator — For processes that give you one number at a time — a batch, an oven, a destructive test. Limits from the mean moving range, run rules evaluated, and an honest note about what an individuals chart cannot see.
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Read next

  • What is Cpk? — Cpk is the distance from your process mean to the nearer specification limit, measured in units of three sigma. Here is what it means, what a good value is, and the three ways it lies to you.
  • Common cause and special cause variation — Every process varies. The question is whether the variation is the process being itself or something happening to it — and answering it wrong is how well-meant intervention makes a process worse.
  • What is a Shewhart chart? — Shewhart chart is the proper name for what most people call a control chart. Here is where it came from, why the limits are at three sigma, and which of the family you need.