Process capability explained: Cp, Cpk, Pp, Ppk in plain English
Process capability tells you whether your process can consistently produce output within specification. It boils down to a small set of numbers — Cp, Cpk, Pp, Ppk — that every CI practitioner needs to know how to compute, read, and challenge. The math is straightforward. The discipline of using them correctly is where most projects go wrong.
The four indices, in one sentence each
- Cp — how wide your spec window is relative to your short-term process spread. Doesn't care if you're centered.
- Cpk — Cp but penalized for being off-center. The smaller of (USL − mean)/3σ and (mean − LSL)/3σ.
- Pp — same as Cp but uses long-term standard deviation (the full historical noise, not just within-subgroup).
- Ppk — same as Cpk but long-term. This is usually the most honest number for a production process that's run for months.
Cp vs Cpk: the visual
Cp answers "can the spread fit?" Cpk answers "does the spread fit AND is it positioned right?" A process can have a high Cp but a low Cpk if its mean has drifted toward one of the spec limits. The reverse can't happen — Cpk is always ≤ Cp.
| Cpk band | Verdict | What it means |
|---|---|---|
| < 1.00 | Not capable | Some output is outside spec. Defects are happening or about to. |
| 1.00 – 1.33 | Marginally capable | Meets spec on average but with no margin for drift. |
| 1.33 – 1.67 | Capable | Comfortable margin. The standard target for most processes. |
| > 1.67 | Highly capable | Significant headroom. Rare in regulated environments. |
Short-term vs long-term variation
The difference between Cp/Cpk and Pp/Ppk is which standard deviation you used. Within-subgroup σ (from a control chart's moving range) is short-term variation — it's the process at its best, in a single hour, with everything stable. Overall σ (from the raw historical data) is long-term — it includes shift changes, lot variation, setup differences, and time-based drift. Long-term σ is usually larger.
- Use Cp/Cpk when you want to know what the process is CAPABLE of when it's behaving.
- Use Pp/Ppk when you want to know what the process is ACTUALLY producing across all conditions.
- Report both. The gap between Cpk and Ppk tells you how much variation is being introduced by long-term factors (shifts, lots, drift).
The rule that keeps capability honest
Capability indices are only meaningful on a process that's in statistical control. If your process is unstable — special causes are firing, points outside control limits, runs above or below the centerline — your capability number is fiction. The math will produce a value; the value won't mean what you think.
Normality assumption (and what to do if it fails)
Standard Cpk math assumes the data is normally distributed. If your process produces skewed or bounded data (e.g., concentricity, particle counts, response times), Cpk computed the normal way will overstate or understate capability. Check normality with a probability plot or Anderson-Darling test. If it fails, options:
- Use non-normal capability methods (Box-Cox transformation, then standard Cpk).
- Report the empirical % out of spec directly rather than a Cpk that assumes normality.
- For bounded data ("can't be negative"), use the appropriate distribution (Weibull, lognormal) and the matching capability index.
How to compute Cpk step-by-step
- Verify the process is in statistical control (run an I-MR or X-bar/R chart). If not, stop. Stabilize first.
- Verify the data is approximately normal (probability plot). If not, transform or switch methods.
- Compute the mean (x̄) and standard deviation (σ). Use long-term σ for Ppk; within-subgroup σ from the MR chart for Cpk.
- Compute Cpk = min[(USL − x̄)/3σ, (x̄ − LSL)/3σ].
- Compare to your target. <1.33 means improvement is needed; report alongside Ppk and the gap between them.
When Cpk numbers lie
Three failure modes that produce plausible-looking but wrong Cpk values:
- Computed on an unstable process — capability is meaningless until special causes are removed.
- Computed on n < 30 — small samples produce wildly variable Cpk; the AIAG standard is 100 measurements minimum for a defensible number.
- Computed assuming normality on non-normal data — the % out of spec implied by the Cpk doesn't match the actual % out of spec.
Reading a capability report from someone else
When a contractor or supplier hands you a Cpk number, the first three things to ask:
- What's the sample size, and over what time window? n < 50 or window < 30 days is suspect.
- Is the underlying process in control? Show me the control chart.
- Was normality tested? If not, the Cpk and the implied defect rate may not match reality.