Problem Solving & Quality · Quality Tools

Process Capability Cp/Cpk

Compare the natural spread of a stable process with the tolerance: Cp says whether it can fit, Cpk whether it is centered enough to do so.

Time45 min
FormatSolo
StageQuality Tools

Process Capability Cp/Cpk: what it is and why it works

Process capability compares the natural spread of a stable process with the width of the tolerance. Cp = (USL − LSL) / 6σ measures potential: whether six standard deviations of process variation could fit inside the tolerance if the process were perfectly centered. Cpk = min(USL − μ, μ − LSL) / 3σ measures actual performance by looking at the distance from the mean to the nearest specification limit. Cp and Cpk use the short-term, within-subgroup standard deviation; the related Pp and Ppk use the overall standard deviation of all data and therefore include drift between subgroups.

The indices turn an argument about a tolerance into a number that everyone can check. A Cpk of 1.0 puts the nearest limit three sigma from the mean, around 0.13 % out of tolerance on that side for a normal process; 1.33 gives four sigma and a much smaller tail. Comparing Cp with Cpk tells you which lever to pull: re-centering when only Cpk is low, variation reduction when both are low. The study depends on two upstream tools: a control chart to prove stability and a gauge R&R to prove that the measured variation is mostly process, not instrument. In DMAIC, capability typically quantifies the baseline in Measure and the gain in Control.

What you need

Specification limits (one or two sided) and the agreed capability requirement
A control chart showing the process is stable over a representative period
An acceptable measurement system for the characteristic
Typically 100 or more individual values, or 25 or more subgroups, covering normal sources of variation
A check of the distribution shape (histogram or normal probability plot)

What you get

Cp and Cpk (and, if required, Pp and Ppk) with the sigma estimate used
An estimate of the expected out-of-tolerance fraction on each side
A diagnosis: centering problem, spread problem, or tolerance worth reviewing
A baseline for measuring the effect of improvements

When to use it

When a specification is disputed and nobody knows if the process can ever meet it.

How to do it, step by step

Confirm first that the process is stable on a control chart — capability of an unstable process means nothing.
Check that the measurement system is adequate and that the data are roughly normal.
Calculate Cp = (USL − LSL) / 6σ: can the spread fit in the tolerance at all?
Calculate Cpk = min(USL − mean, mean − LSL) / 3σ: does it fit where the process is actually centered?
Compare with the agreed requirement — often 1.33 for running processes — and decide: center, reduce variation, or review the tolerance.

Worked example: A disputed bore tolerance at an aerospace machining supplier

Illustrative scenario — figures are realistic but not from a real company.

A machining supplier produces aluminum actuator housings with a critical bore of 1.2500 in ±0.0010 in. The customer required Cpk ≥ 1.33, and the supplier's engineering team claimed the tolerance was unrealistic after several rejected lots.

An X-bar and R chart with subgroups of five over 25 subgroups showed the process was stable, with no points outside limits or unusual runs.
A gauge R&R on the air gauge gave 8 % of tolerance, so the measurement system was acceptable. The histogram looked roughly normal.
Within-subgroup sigma was 0.00020 in. Cp = 0.0020 / (6 × 0.00020) = 1.67, so the spread fits comfortably. The mean was 1.25055 in, giving Cpk = (1.2510 − 1.25055) / (3 × 0.00020) = 0.75.
The gap between Cp and Cpk pointed to centering, not tolerance. Investigation found the tool offset was set toward the upper end on purpose, to leave material for a hand-finishing step that had since been eliminated.

Result. After the offset was corrected to target, 30 new subgroups gave a mean of 1.25004 in and Cpk of 1.60. The supplier dropped its request for a wider tolerance, and rejected lots stopped. What the team learned is that most capability disputes should begin by comparing Cp with Cpk before anyone argues about the drawing.

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Common pitfalls and how to avoid them

Calculating Cpk on an unstable process and quoting it as a property of the machine.Confirm stability on a control chart first; if special causes are present, remove them before reporting capability.
Assuming normality for skewed data such as flatness, runout or impurity levels bounded at zero.Check the distribution; for non-normal data, use a suitable distribution fit or percentile-based method and state which one.
Mixing up Cpk and Ppk, or computing sigma from all data and calling the result Cpk.State the sigma used: within-subgroup for Cp and Cpk, overall for Pp and Ppk, and report both when drift matters.
Using a few dozen parts from one shift to approve a process for years.Collect data over enough time to include normal shifts, material lots and tool changes, and add a confidence interval when the sample is small.

Frequently asked questions

What is the difference between Cp and Cpk?

Cp compares the tolerance width with the process spread and ignores where the process is centered, so it shows potential capability. Cpk compares the distance from the mean to the nearest specification limit with half the spread, so it shows actual capability. When Cp and Cpk are equal, the process is centered. When Cpk is much lower than Cp, re-centering the process will usually recover most of the gap.

What is a good Cpk value?

A Cpk of 1.33 is a common minimum for running processes, meaning the nearest specification limit sits four standard deviations from the mean. Many automotive customers ask for 1.67 on new processes or special characteristics. A Cpk below 1.0 means a visible fraction of output falls outside tolerance. The right target is whatever the customer and your quality agreement specify.

What is the difference between Cpk and Ppk?

Both use the same formula, but Cpk uses the within-subgroup standard deviation, which reflects short-term variation, while Ppk uses the overall standard deviation of all data, which includes shifts and drifts between subgroups. If Ppk is much lower than Cpk, the process moves over time, and a control chart will usually show where. Customers often request Ppk for initial studies and Cpk for ongoing monitoring.

Origin

Process capability indices Cp / Cpk — statistical quality control practice, formalized in the literature in the 1980s (e.g. V. E. Kane, Journal of Quality Technology, 1986).

Used in these playbooks

Process stability review 2 weeks

Two weeks to find out whether a disputed characteristic is a measurement, stability or capability problem — and to lock the answer into the control plan.

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