Cp vs Cpk — why a centered process is not the same as a capable one
Cp and Cpk get quoted interchangeably and they are not the same number. The gap between them is the single most useful thing a capability study tells you, and most reports bury it.
Cp measures whether a process's spread fits inside the specification window: (USL − LSL) / 6σ. Cpk also accounts for centering — it's the distance from the process mean to the nearest spec limit, divided by 3σ. A process can have a great Cp and a poor Cpk if it's tightly controlled but off-center. The common rule of thumb: Cpk ≥ 1.33 is capable, 1.00–1.33 is marginal, below 1.00 is producing out-of-spec parts. When Cp stays high but Cpk drops, the spread is fine — the process has drifted off-center.
What each number is asking
Cp asks a question about spread: if the process were perfectly centered, would its natural variation fit inside the tolerance? It's the ratio of the spec width to six standard deviations. But Cp is blind to location — a process humming along entirely off to one side can still post a high Cp.
Cpk asks about spread and centering: it takes the smaller of the two distances from the mean to each spec limit and divides by 3σ. Because it uses the nearest limit, drifting toward either limit drags Cpk down even though Cp hasn't moved. Cpk ≤ Cp always, and they're equal only when the process is perfectly centered.
How to read the gap
Cp high, Cpk low → re-center, don't re-tool
This is the most actionable pattern in capability analysis. A large Cp−Cpk gap means your variation is fine; you're just off-center. The fix is an offset adjustment, not a hunt for new variation sources. Reading only Cpk would send you chasing the wrong problem.
Cp and Cpk both low → reduce variation
If the spread itself doesn't fit, centering won't save you. Now it's a genuine variation-reduction problem — tooling, material, method.
Capability ladders to defect rate
Capability maps to parts-per-million out of spec. A centered Cpk of 1.0 is about 2,700 ppm; 1.33 is about 63 ppm; 1.67 approaches the few-ppm range. Quoting the ppm alongside the index makes the stakes concrete.
Common mistakes
- Reporting Cpk without Cp. The two together tell you whether to re-center or reduce variation; Cpk alone hides which.
- Computing capability on an unstable process. Capability assumes the process is in statistical control. Run the control chart first — capability on an out-of-control process is meaningless.
- Confusing Cpk with Ppk. Cpk uses short-term within-subgroup sigma; Ppk uses long-term overall sigma. A healthy Cpk with a lagging Ppk means between-shift drift is eating your margin.
- Non-normal data. The standard formulas assume normality. Skewed or bounded data needs a transformation or a non-normal capability method.
Where this gets slow by hand
One capability study is a quick calculation. Across dozens of characteristics, multiple lines, and every incoming lot — first verifying control, checking normality, then computing Cp, Cpk, Pp, Ppk and ppm for each — it becomes a standing reporting burden, and the Cp−Cpk gap that should drive action gets flattened into a single pass/fail number.
Capability that starts by checking control
Niobia computes Cp, Cpk, Pp, Ppk and the implied ppm for every characteristic — but first verifies the process is in statistical control and tests the distribution, so the indices mean something. It surfaces the Cp−Cpk gap explicitly, telling you whether the move is to re-center or to reduce variation, and tracks capability over time so a slow drift shows up before it crosses a limit. The result is the decision, not a spreadsheet of indices.
Frequently asked
What is the difference between Cp and Cpk?
Cp measures whether a process's spread fits within the spec limits, ignoring where it's centered: (USL minus LSL) divided by six sigma. Cpk also accounts for centering — the distance from the process mean to the nearest spec limit divided by three sigma. Cpk is always less than or equal to Cp, and they're equal only when the process is perfectly centered.
What is a good Cpk value?
A common rule of thumb is that Cpk of at least 1.33 indicates a capable process, 1.00 to 1.33 is marginal, and below 1.00 means the process is producing out-of-spec parts. Higher requirements (1.67 or 2.0) are used for safety-critical characteristics.
Why is my Cpk low when my Cp is high?
Because the process is off-center. Cp only looks at spread, so it stays high if variation is small; Cpk uses the distance to the nearest spec limit, so it collapses as the mean drifts toward a limit. The fix is to re-center the process, not to reduce variation.