Lean Six Sigma · Beginner · 15 min read

Control Charts, Explained

Lean Six Sigma

Every process wiggles. The skill is knowing which wiggles are just noise — and which are the process telling you something changed. A control chart is the tool that makes that call for you: it draws the boundaries of normal variation, so real shifts stand out before they become defects.

Why this matters at work: without a control chart, teams either overreact to noise (adjusting a healthy process and making it worse) or underreact to real change (finding out from customer complaints). Control charts are the workhorse of the DMAIC Control phase, the gateway to capability analysis, and a guaranteed topic on the ASQ CSSBB and CQE exams.

By the end, you should be able to

Distinguish common-cause variation (noise) from special-cause variation (signal), and explain why each demands a different response.
Read a control chart: centre line, control limits, and the classic out-of-control patterns.
Compute I-MR control limits from data and build the chart in Excel and Minitab.
Explain why control limits and specification limits are completely different things.

Before you start

You’ll get the most from this lesson after The Normal Distribution: Meet the Bell Curve — control limits are the ±3σ idea applied over time. Its partner lesson, Process Capability (C_p & C_pk), is the natural next step: capability asks “does the process fit the spec?”, while control charts ask “is the process staying itself?” — and capability is only meaningful once this lesson’s answer is yes.

Two kinds of variation

Common cause — the noise

The everyday wiggle built into how the process works: tiny differences in material, temperature, timing, technique. It’s always present, it’s stable, and it’s predictable as a band even though individual points aren’t. Responding to individual common-cause wiggles is called tampering — and it adds variation.

Special cause — the signal

Something outside the usual system: a new material lot, a worn tool, a changed setting, a new operator’s method. Special causes are assignable — you can find them — and they’re exactly what you should chase, quickly, while the trail is fresh.

One sentence to remember: react to signals by investigating the cause; react to noise only by improving the whole system. Confusing the two is the most expensive mistake in process management.

Anatomy of a control chart

A control chart is your measurement plotted in time order, with three horizontal lines:

Centre line (CL) — the process average.
Upper and lower control limits (UCL, LCL) — drawn at ±3σ of the plotted statistic. For a stable process, 99.73% of points fall between them, so a point outside is a genuine rarity — a signal, not noise.

The limits are computed from the process’s own data — they are the voice of the process. Nobody chooses them, and that’s the point: the chart defines “normal for this process” and then flags departures from it.

Interactive: control chart simulator

Below is an individuals chart for a stable process. Use the buttons to inject different kinds of trouble and watch how the chart catches each one — flagged points turn red, and the status line names the rule that fired.

Stable: all points inside the limits with no suspicious patterns. This is what “in control” looks like — leave it alone.

The detection rules

A point beyond a limit is the loudest signal, but not the only one. Patterns inside the limits can also be too unlikely to be chance. The three rules this lesson’s simulator uses are the classics:

Core out-of-control tests (from the Western Electric / Nelson rule sets)
Rule	Pattern	What it usually means
Rule 1	Any point beyond the ±3σ control limits	A sudden special cause: a mistake, a broken tool, a bad lot
Rule 2	Eight (or more) consecutive points on the same side of the centre line	The process mean has shifted to a new level
Rule 3	Six (or more) consecutive points steadily rising or falling	A drift: tool wear, temperature creep, gradual contamination

Software (and the full rule sets) add more patterns, but these three catch the overwhelming majority of real-world signals — and they’re the ones exams ask about.

Choosing the right chart

The chart type follows from two questions: what kind of data? and how is it collected?

The common control charts and when to use them
Chart	Data type	Use when
I-MR (individuals & moving range)	Continuous, one value at a time	Slow or one-at-a-time processes: daily yields, batch results, monthly metrics
X̄-R (average & range)	Continuous, small subgroups	Samples of 2–8 taken together, e.g. five parts each hour
X̄-S (average & standard deviation)	Continuous, larger subgroups	Subgroups of 9 or more, where S beats R as a spread estimate
p / np	Attribute: defective units (yes/no)	Fraction (p) or count (np) of defective items per sample
c / u	Attribute: defect counts	Number of defects per unit — c for constant sample size, u for varying

This lesson works with the I-MR chart throughout: it’s the most broadly useful, and every other variables chart is the same idea with subgroups.

How to build an I-MR chart

Collect 20–25 individual measurements in time order from routine operation — no cherry-picking good days.
Compute the moving ranges: MR_i = |x_i − x_i−1|, the gap between each point and the previous one.
Average both: the process mean x̄ and the mean moving range M̄R.
Compute the limits for the individuals chart: UCL = x̄ + 2.66 × M̄R and LCL = x̄ − 2.66 × M̄R (2.66 converts the average moving range into a 3σ distance). The MR chart’s own upper limit is 3.267 × M̄R.
Plot, then apply the rules. If signals appear, find and fix their causes and recompute the limits from clean data.
Extend the limits forward and judge every new point against them — the chart is now a live alarm system, not a report.

Worked example: daily fill weights

The coffee-bag line from the capability lesson weighs one bag each morning. Twenty-five days give a mean of x̄ = 500.4 g and an average moving range of M̄R = 1.2 g.

UCL = 500.4 + 2.66 × 1.2 = 500.4 + 3.19 = 503.59 g.
LCL = 500.4 − 3.19 = 497.21 g.
On day 26 the bag weighs 504.1 g — above the UCL. Rule 1 fires.
Investigation the same morning finds a new operator zeroed the filler against the wrong tare weight. Ten minutes to fix — instead of a week of overfilled bags discovered at month-end stock-take.

Notice: 504.1 g is still inside the specification (506 g). The chart caught the change while product was still good — that early warning is the entire value of control charting.

Control limits are not spec limits

The distinction exams (and auditors) love to test
	Control limits	Specification limits
Set by	The process’s own data (±3σ)	The customer, drawing, or regulation
Question answered	“Has the process changed?”	“Is this unit acceptable?”
Voice of…	The process	The customer
Drawn on the chart?	Yes — they define the chart	No — specs belong in capability analysis

The two tools together: a control chart proves the process is stable; a capability study then asks whether that stable process is good enough for the spec. In control ≠ capable — a process can be perfectly stable at producing 10% scrap.

Common mistakes

Drawing spec limits on the control chart. It invites judging stability by customer limits — two unrelated questions. Keep specs in the capability analysis where they belong.

Tampering. Adjusting the process after every point that isn’t exactly on target treats noise as signal — and provably increases variation. If no rule fires, hands off.

Recalculating limits with every new batch of data. Limits are a fixed yardstick from a known-stable period. Recompute them only after a deliberate, verified process change — otherwise the chart slowly learns to accept degradation.

Declaring victory at “in control.” Stability means consistent, not good. The follow-up question is always capability.

Statistics implementation: Excel and Minitab

Software should confirm and speed up what you now understand — not replace the thinking.

Excel functions

Excel has no built-in control chart, but an I-MR chart is a few formulas plus a line chart:

Excel functions for I-MR control charts (Formulas › More Functions › Statistical)
Function	Syntax	Purpose	When to use
`AVERAGE`	`=AVERAGE(range)`	Centre line x̄ and the mean moving range M̄R	Always — both averages the limits are built from
`ABS`	`=ABS(A3-A2)`	Each moving range \|x_i − x_i−1\|	Filled down beside the data to create the MR column
`STDEV.S`	`=STDEV.S(range)`	Overall sample standard deviation	Sanity checks only — chart limits use M̄R × 2.66, not 3 × STDEV.S, because the moving range estimates short-term variation
`MAX` / `MIN`	`=MAX(range)`, `=MIN(range)`	Quick scan of extremes	Spotting Rule-1 candidates before charting
`COUNTIF`	`=COUNTIF(range,">"&UCL)`	Count of points beyond a limit	Flagging Rule-1 violations automatically
`IF`	`=IF(OR(A2>UCL,A2<LCL),A2,NA())`	A helper column of only the violating points	Plotting signals as a separate red series on the chart

Excel use cases

With 25 measurements in A2:A26:

Moving ranges: in B3 enter =ABS(A3-A2) and fill down to B26.
Averages: =AVERAGE(A2:A26) in E1 (x̄), =AVERAGE(B3:B26) in E2 (M̄R).
Limits: =E1+2.66*E2 (UCL) and =E1-2.66*E2 (LCL) — the fill-weight data gives 503.59 and 497.21.
The chart: plot column A as a line; add three flat series for CL/UCL/LCL; add the IF helper column as a markers-only series in red. New rows extend the chart into a live monitor.

Minitab navigation

Minitab menu paths for control charts
Menu path	What it gives you	When to choose it
Stat › Control Charts › Variables Charts for Individuals › I-MR	The individuals and moving-range pair used throughout this lesson	Your default for one-at-a-time continuous data
Stat › Control Charts › Variables Charts for Subgroups › Xbar-R	Averages and ranges of small subgroups	Samples of 2–8 collected together (switch to Xbar-S for 9+)
Stat › Control Charts › Attributes Charts › P / NP / C / U	Charts for defectives and defect counts	Pass/fail or count data instead of measurements
Stat › Quality Tools › Capability Sixpack › Normal	Control charts, normality check, and capability in one view	The stability-then-capability workflow in a single command

In the I-MR dialog, enter the data column, then open I-MR Options › Tests and select which detection rules to apply — “Perform all tests for special causes” enables the full Nelson set. Minitab marks each violating point with the number of the test that fired.

Exam tips (ASQ CSSBB / CQE)

Know the I-MR constants cold: UCL/LCL = x̄ ± 2.66 M̄R, and the MR chart’s UCL = 3.267 M̄R. For X̄-R charts, limits use A₂, D₃, D₄ from the constants table the exam provides — practice reading that table quickly.
Control vs spec limits is a near-guaranteed question: control limits come from the process (±3σ), spec limits from the customer, and specs never appear on a control chart.
“In control” ≠ “capable” — and stability is the prerequisite for capability analysis, not the other way round.
Chart selection follows data type: continuous → I-MR / X̄-R / X̄-S by subgroup size; defectives (yes/no) → p or np; defect counts → c or u. Expect at least one “which chart?” scenario.
Tampering (over-adjustment) increases variation — Deming’s funnel experiment is the classic reference if the question names it.
Rules: memorise the big three — 1 beyond 3σ, 8 in a row one side, 6 trending — and recognise that patterns inside the limits can still be signals.

Try it yourself

A lab logs one purity result per batch. Twenty-four batches give x̄ = 50.0 and M̄R = 1.2. Compute the individuals-chart limits to two decimal places.

Your UCL:

Your LCL:

Final summary

Common cause is the built-in noise; special cause is an assignable change. Each demands the opposite response.
A control chart plots data in time order against CL and ±3σ control limits computed from the process itself.
The big three rules: beyond a limit, 8 one side, 6 trending — patterns inside the limits can be signals too.
I-MR limits: x̄ ± 2.66 × M̄R; chart choice follows data type and subgrouping.
Control limits are the voice of the process; spec limits the voice of the customer — never draw specs on the chart.
In control ≠ capable: stability first, then a capability study.

If you remember one thing: the chart’s job is to tell you when to act and when to leave the process alone — and doing either at the wrong time makes things worse.

References & further reading

NIST/SEMATECH e-Handbook of Statistical Methods — Univariate and Multivariate Control Charts: itl.nist.gov/div898/handbook
ASQ Quality Resources — Control Chart: asq.org/quality-resources/control-chart
Montgomery, D. C., Introduction to Statistical Quality Control — the standard reference on SPC and the control chart constants.

Control Charts, Explained

By the end, you should be able to

Before you start

Two kinds of variation

Common cause — the noise

Special cause — the signal

Anatomy of a control chart

Interactive: control chart simulator

The detection rules

Choosing the right chart

How to build an I-MR chart

Worked example: daily fill weights

Control limits are not spec limits

Common mistakes

Statistics implementation: Excel and Minitab

Excel functions

Excel use cases

Minitab navigation

Exam tips (ASQ CSSBB / CQE)

Try it yourself

Check your understanding

Final summary

References & further reading