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Lean Six Sigma · Beginner · 15 min read

Process Capability: Will Your Process Meet the Spec?

Lean Six Sigma

Your customer sets the goalposts. Your process kicks the ball. Process capability measures — with two simple numbers, Cp and Cpk — whether your process can reliably land inside those goalposts.

Why this matters at work: capability indices are the standard language between suppliers and customers. A contract that says “maintain Cpk ≥ 1.33” is a precise, testable promise about defect rates — and knowing how to compute and read these numbers is a core skill for quality roles and a guaranteed topic on the ASQ CSSBB and CQE exams.

By the end, you should be able to

  • Explain what process capability compares: the customer’s specification width against the process’s natural spread.
  • Calculate Cp and Cpk from a mean, a standard deviation, and specification limits.
  • Interpret the results against the common benchmarks (1.00, 1.33, 1.67) and spot an off-centre process.
  • Run a capability analysis in Excel and Minitab and know which menu option to pick.

Before you start

This lesson builds directly on The Normal Distribution: Meet the Bell Curve. You should be comfortable with the mean μ, the standard deviation σ, and the idea that almost all values of a normal process fall within ±3σ of the mean. That “±3σ” span — 6σ wide in total — is the star of this lesson.

Two voices: the customer and the process

Every capability question is a conversation between two voices:

Voice of the customer — the specification

The customer (or the drawing, or the regulation) states what is acceptable: a lower specification limit (LSL) and an upper specification limit (USL). A coffee roaster promising “500 g ± 6 g” has set LSL = 494 g and USL = 506 g. The distance between them, USL − LSL, is the specification width — the width of the goalposts.

Voice of the process — the natural spread

The process doesn’t care what the drawing says. It produces values with its own mean μ and standard deviation σ. For a stable, roughly normal process, essentially all output (99.73%) lands within μ ± 3σ — a natural spread that is 6σ wide.

Capability is the comparison of the two widths. If the goalposts (spec width) are much wider than the ball’s scatter (6σ), nearly everything lands in-spec. If the scatter is as wide as the goalposts — or the aim is off-centre — defects follow.

One sentence to remember: Cp asks “is the spread small enough?” and Cpk asks “is the spread small enough where the process is actually aimed?”

Terminology

The words you’ll meet in every capability discussion
TermMeaningPlain-language version
LSL / USLLower / upper specification limitThe goalposts set by the customer
Specification widthUSL − LSLHow far apart the goalposts are
Natural process spread6σ (from μ − 3σ to μ + 3σ)How widely the process scatters its output
CpPotential capabilityCould the process fit, if perfectly centred?
CpkActual capabilityDoes it fit, given where it’s actually aimed?
Pp / PpkPerformance indices (overall σ)Same idea, computed with long-term variation
Stable / in controlOnly common-cause variation presentThe process behaves the same way over time

The formulas: Cp and Cpk

Cp is a simple ratio of the two widths: specification width on top, natural process spread underneath. Cp = 1 means the goalposts and the scatter are exactly the same width — the process barely fits, with zero room for error. Cp = 2 means the goalposts are twice as wide as the scatter. But Cp has a blind spot: it completely ignores where the process is centred. A process aimed way off-target can still have a beautiful Cp.

Cpk fixes the blind spot. It measures the distance from the process mean to the nearest spec limit, in units of 3σ, and reports the worse side. If the process is perfectly centred, Cpk = Cp. The further the mean drifts toward a limit, the lower Cpk falls — even while Cp stays put. That gap between the two numbers is itself a diagnosis:

Cp high but Cpk low? The spread is fine — the process is simply off-centre. Re-aim it (usually the cheap fix). Both low? The spread itself is too wide — you have a variation-reduction project on your hands (the expensive fix).

Interactive: capability explorer

Move the sliders and watch both indices react. Try this experiment: leave the spread alone and slide the mean off-centre — Cp won’t budge, but Cpk will sink. Then re-centre the mean and widen σ instead — now both fall together.

LSL USL μ
Cp1.33
Cpk1.33
Out of spec≈ 63 ppm

Capable: Cpk meets the common 1.33 benchmark.

How to run a capability study, step by step

  1. Confirm the process is stable first. Run a control chart (see Control Charts Explained). Capability numbers from an unstable process are fiction — the spread you measure today won’t be the spread you get tomorrow.
  2. Check the data are roughly normal. A histogram or normal probability plot is enough at this level. Strongly skewed data need a transformation or a different method before the formulas apply.
  3. Collect enough data. Aim for at least 30 measurements — 50 to 125 is better — taken across a representative stretch of production, not one lucky hour.
  4. Compute μ and σ. Use the sample mean and sample standard deviation (or an estimate from a control chart’s subgroups — that distinction becomes Cpk vs Ppk later).
  5. Apply the formulas. Cp from the two widths; Cpk from the nearest-limit distance.
  6. Interpret and act. Compare against the agreed benchmark, then diagnose: centring problem, spread problem, or both.

Worked example: the coffee bag line

A packing line fills 500 g coffee bags with a spec of 500 ± 6 g (LSL = 494, USL = 506). Sixty bags from a stable run give a mean of μ = 501.2 g and a standard deviation of σ = 1.5 g.

  1. Specification width: 506 − 494 = 12 g.
  2. Natural spread: 6σ = 6 × 1.5 = 9 g.
  3. Cp = 12 / 9 = 1.33. Potential looks healthy: the goalposts are a third wider than the scatter.
  4. Upper side: (506 − 501.2) / (3 × 1.5) = 4.8 / 4.5 = 1.07.
  5. Lower side: (501.2 − 494) / 4.5 = 7.2 / 4.5 = 1.60.
  6. Cpk = min(1.07, 1.60) = 1.07.

The story the two numbers tell: the spread is fine (Cp = 1.33), but the line is overfilling by 1.2 g on average, pushing output toward the upper limit and dragging Cpk down to 1.07 — below the 1.33 benchmark. The fix isn’t a costly variation-reduction project; it’s re-targeting the filler back to 500 g. Centre it, and Cpk rises to meet Cp at 1.33 — and the overfill give-away stops too.

Reading the numbers

Common Cpk benchmarks (two-sided specs, normal, stable process)
CpkRoughly how many out of specTypical reading
< 1.00More than ~2,700 ppmNot capable — the process cannot reliably hold the spec
1.00~2,700 ppm (centred)Barely fits — any drift creates defects immediately
1.33~63 ppmThe classic minimum most customers require
1.67~0.6 ppmStrong — typical target for safety-critical characteristics
2.00~0.002 ppm“Six Sigma” capability with the mean on target
Why 1.33? It means the nearest spec limit sits 4σ away from the mean (because 4/3 = 1.33) — a full extra σ of safety margin beyond “barely fits.” That buffer absorbs the small drifts every real process has.

One more distinction you’ll meet immediately in software: Cpk vs Ppk. Cpk uses the within-subgroup (short-term) σ estimated from a control chart; Ppk uses the overall (long-term) standard deviation of all the data. Ppk is usually a little lower, because long-term data picks up the small shifts between subgroups. Minitab prints both — now you know why they differ.

Common mistakes

Computing capability on an unstable process. If the control chart shows special causes, the σ you measured is a moving target and the index is meaningless. Stability first, capability second — always.
Quoting Cp when the process is off-centre. Cp is blind to centring. Reporting “Cp = 1.6, we’re fine” while Cpk is 0.7 hides a real defect stream. Report both; act on Cpk.
Forcing the formulas onto non-normal data. The ppm predictions in the table assume a normal shape. Cycle-time and flatness data, for example, are often skewed — transform first or use a non-normal capability method.
Confusing 6σ in the denominator with “Six Sigma” the programme. The 6σ in Cp is simply the width of the natural spread. “Six Sigma quality” refers to specs sitting six standard deviations from the mean — Cp = 2.0 territory.

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 Cp/Cpk function — you assemble them from these pieces:

Excel functions for capability analysis (Formulas › More Functions › Statistical)
FunctionSyntaxPurposeWhen to use
AVERAGE =AVERAGE(range) Process mean μ Always — the first ingredient of every capability formula
STDEV.S =STDEV.S(range) Sample standard deviation Your default: measurement data is a sample of the process, not the whole population
STDEV.P =STDEV.P(range) Population standard deviation Only when the range truly is the entire population — rare in capability work
MIN =MIN(a, b) Picks the worse side The “min” in the Cpk formula: nearest-limit side wins
NORM.DIST =NORM.DIST(x, mean, sd, TRUE) Probability of a value below x Estimating the out-of-spec fraction below the LSL
NORM.S.DIST =NORM.S.DIST(z, TRUE) Same, from a z-score When you’ve already standardised (z = (limit − μ)/σ)
COUNTIFS =COUNTIFS(range,"<"&LSL) + COUNTIFS(range,">"&USL) Actual out-of-spec count Sanity-checking the model’s ppm prediction against the raw data

Excel use cases

With data in A2:A61, and E1 = LSL, E2 = USL:

  1. Mean and spread: =AVERAGE(A2:A61) in E4, =STDEV.S(A2:A61) in E5.
  2. Cp: =(E2-E1)/(6*E5) — the coffee-bag data returns 1.33.
  3. Cpk: =MIN((E2-E4)/(3*E5), (E4-E1)/(3*E5)) — returns 1.07, flagging the off-centre fill.
  4. Predicted out-of-spec: =NORM.DIST(E1,E4,E5,TRUE) + (1-NORM.DIST(E2,E4,E5,TRUE)), formatted as a percentage (multiply by 1,000,000 for ppm).

Minitab navigation

Minitab menu paths for capability analysis
Menu pathWhat it gives youWhen to choose it
Stat › Quality Tools › Capability Analysis › Normal The classic single report: histogram with spec limits, Cp/Cpk (within) and Pp/Ppk (overall), plus expected ppm Your standard choice once stability is already confirmed — the report customers expect
Stat › Quality Tools › Capability Sixpack › Normal Control charts, normality plot, and capability in one six-panel view Best first run: it checks the stability and normality assumptions and the capability together
Stat › Quality Tools › Capability Analysis › Nonnormal Capability using a fitted distribution (e.g. Weibull, lognormal) When the normality check fails and a transformation isn’t appropriate
Graph › Probability Plot Quick normality check on its own Fast assumption screening before any capability run

In the dialog, enter your data column, the subgroup size (enter 1 for individual measurements), and the LSL/USL. Minitab estimates the within-subgroup σ for Cpk and the overall σ for Ppk — which is exactly why the two sets of indices differ on the report.

Exam tips (ASQ CSSBB / CQE)

  • Memorise both formulas cold. Exam questions hand you μ, σ, LSL, USL and expect Cp and Cpk in under a minute. Practice until the coffee-bag example takes you 30 seconds.
  • Know the signature patterns: Cp = Cpk ⇒ perfectly centred; Cp > Cpk ⇒ off-centre; Cpk can never exceed Cp. A negative Cpk means the mean is outside a spec limit.
  • One-sided specs: with only a USL, Cpk = (USL − μ)/3σ and Cp is undefined — a favourite exam trap.
  • Short-term vs long-term: Cp/Cpk pair with within-subgroup (short-term) σ; Pp/Ppk with overall (long-term) σ. Questions about “which index uses which sigma” appear on both exams.
  • Benchmarks: 1.00 ≈ 2,700 ppm, 1.33 ≈ 63 ppm, 1.67 ≈ 0.6 ppm (centred, two-sided). Knowing 1.33 ⇔ “4σ to the nearest limit” lets you re-derive the rest.
  • Prerequisites are testable: “What must be true before a capability study?” — stability (in control) and approximate normality. Stability always comes first.

Try it yourself

A machining line cuts shafts to a diameter spec of 10.0 ± 0.5 mm (LSL = 9.5, USL = 10.5). A stable run gives μ = 10.1 mm and σ = 0.12 mm. Compute both indices to two decimal places.

Check your understanding

Five questions. Pick an answer for each, then press Check my answers.

1. What does Cp compare?
2. A process has Cp = 1.60 but Cpk = 0.70. What is the most likely diagnosis?
3. LSL = 20, USL = 30, μ = 27, σ = 1. What is Cpk?
4. What must be confirmed before a capability study is meaningful?
5. Why is Cpk ≥ 1.33 the classic customer requirement rather than 1.00?

Final summary

  • Capability compares the voice of the customer (spec width) with the voice of the process (6σ spread).
  • Cp = (USL − LSL) / 6σ measures potential; it ignores centring.
  • Cpk = min[(USL − μ)/3σ, (μ − LSL)/3σ] measures reality; it reports the worse side.
  • A gap between them is a diagnosis: re-aim if only Cpk is low, reduce variation if both are.
  • Benchmarks: 1.00 barely fits, 1.33 the classic requirement, 1.67 safety-critical territory.
  • Stability first, capability second — and check normality before trusting the ppm predictions.
If you remember one thing: Cp asks whether the process could fit the spec; Cpk tells you whether it actually does. Report both — the gap between them tells you what to fix.

References & further reading

  • NIST/SEMATECH e-Handbook of Statistical Methods — Process Capability: itl.nist.gov/div898/handbook
  • ASQ Quality Resources — Process Capability (Cp, Cpk): asq.org/quality-resources
  • Montgomery, D. C., Introduction to Statistical Quality Control — the standard reference chapter on capability indices.