🏭 CSSGB Quest › Learn

Process capability: Cp, Cpk, DPMO

Process capability measures how well a process fits within its specification limits. A capable process consistently produces output within spec without requiring sorting or rework. Cp and Cpk are the standard indices; DPMO and sigma level translate capability into defect rates.

Key definitions

Term	Symbol	Meaning
Upper spec limit	USL	Maximum acceptable value
Lower spec limit	LSL	Minimum acceptable value
Process mean	μ or x̅	Average of measured values
Process std dev	σ or s	Spread of the process output
Spec width	USL − LSL	Total tolerance allowed

Cp: potential capability

Cp compares the width of the specification to the width of the process. It assumes the process is centered on the target.

Cp = (USL - LSL) / (6σ)

Cp ≥ 1.33: commonly accepted as capable (spec limits at least 4σ from a centered mean)
Cp = 1.0: exactly fits (3σ on each side; about 0.27% out of spec if normal and centered)
Cp < 1.0: process is wider than the spec; defects are inevitable

Cp ignores centering. A process can have a high Cp but still produce many defects if it is off-center.

Cpk: actual capability

Cpk accounts for both spread and centering. It is always ≤ Cp.

Cpk = min[ (USL - x̄) / (3σ), (x̄ - LSL) / (3σ) ]

Cpk = Cp when the process is perfectly centered
Cpk < 0: the process mean is outside a spec limit
Cpk = 1.33 is a common minimum target (customers and industries set their own)

Worked example: Examplorphine fill weight

Spec: 245–255 mg (LSL = 245, USL = 255)
Process data: x̅ = 251.5 mg, s = 1.2 mg

Cp = (255 - 245) / (6 × 1.2) = 10 / 7.2 = 1.39 Cpk = min[ (255 - 251.5) / (3 × 1.2) → 3.5 / 3.6 = 0.97, (251.5 - 245) / (3 × 1.2) → 6.5 / 3.6 = 1.81 ] Cpk = 0.97 ← limited by the upper tail

Interpretation: The process has sufficient spread (Cp = 1.39) but is shifted high. The upper tail will produce defects above 255 mg. Action: re-center the process to the target (250 mg).

Sigma level and DPMO

DPMO (Defects Per Million Opportunities) and sigma level provide a universal quality language across industries.

Sigma level	DPMO	Yield
2σ	308,537	69.15%
3σ	66,807	93.32%
4σ	6,210	99.38%
5σ	233	99.977%
6σ	3.4	99.9997%

The 6σ DPMO of 3.4 assumes a 1.5σ long-term shift of the process mean from target — the "Six Sigma shift." A truly centered process at 6σ would produce ~0.002 DPMO.

DPMO = (Defects / (Units × Opportunities per unit)) × 1,000,000

Pp and Ppk (performance indices)

Pp and Ppk use the overall standard deviation (all data combined) rather than the within-subgroup estimate. They answer "how has this process performed historically?" Cp/Cpk use the within-subgroup estimate and answer "what is this process capable of when in control?"

Index pair	Uses	Answers
Cp / Cpk	Within-subgroup σ̂	Potential capability (when stable)
Pp / Ppk	Overall sample std dev s	Actual performance (historical)

Common exam traps

Cp and Cpk only apply to stable, in-control processes. Calculate capability after confirming statistical control (run chart or control chart). An unstable process has a meaningless Cpk.
Cpk ≤ Cp always. If your calculation gives Cpk > Cp, check your math.
Cpk = 1.0 is not great. For a centered normal process (Cp = Cpk = 1.0) about 0.27% (2,700 ppm) falls outside spec; an off-center process with Cpk = 1.0 has about 0.135% beyond the nearer limit. Cpk ≥ 1.33 is a common minimum.
The 6σ goal is 3.4 DPMO, not zero defects per se. It incorporates a 1.5σ shift for long-term drift.

Test yourself

The free 20-question CSSGB diagnostic covers all six Body of Knowledge sections, with an explanation for every answer.

Take the free CSSGB diagnostic

More: Basic statistics · MSA · Control charts · Data types · Run charts

CSSGB Quest by Bizarre Act. Original study material; not affiliated with ASQ. CSSGB is a certification of ASQ. Terms · Privacy