Pp / Ppk
Within-subgroup sigma vs the full long-term spread.
Cpk measures capability over short-term, within-subgroup variation; Ppk measures performance over the full, long-term spread. When Ppk lags Cpk, the gap is the between-shift and between-day drift that a short-term study never sees, quietly eating your margin.
What it measures
Capability and performance use the same formulas with a crucial difference in which sigma they put in the denominator:
- Cpk (capability) uses short-term, within-subgroup sigma, estimated from the variation inside rational subgroups (typically from R̄/d₂). It describes the process at its best: what it can do when only common-cause, moment-to-moment variation is present.
- Ppk (performance) uses overall, long-term sigma, the standard deviation of all the individual data over the full study. It describes the process as it actually ran, including shift changes, material lots, and slow drift.
- Both indices take the same form: min[(USL − μ)/3σ, (μ − LSL)/3σ], the distance from the mean to the nearer spec limit in units of 3 sigma. Only the sigma differs, within-subgroup for Cpk, overall for Ppk.
So Cpk and Ppk are two readings of the same process: its instantaneous best and its lived reality. The relationship between them is the diagnostic.
How to read the output
Read the two together. When Cpk and Ppk are close, the process is stable: its long-term spread is barely wider than its moment-to-moment spread, so there is little drift between subgroups. When Ppk lags well behind Cpk, the process is capable in any given moment but wanders over time, between shifts, between days, between lots, and that wander is eating margin that a short-term capability study would have told you was comfortable. The fix differs by case: a low Cpk means the inherent process is too variable or off-center and needs a fundamental change; a healthy Cpk with a poor Ppk means the process is fine but uncontrolled, and the answer is control charts and stabilization, not a new process.
A real use case
A cell assembly step reports a comfortable Cpk of 1.6 on a seal-thickness characteristic from a capability study run over two hours on one shift. In production it keeps producing occasional out-of-spec parts, which makes no sense against a 1.6 Cpk, until the Ppk is computed over three weeks of data and comes back at 1.1. The within-shift process is genuinely capable; the long-term performance is not, because the mean shifts between shifts and drifts with humidity across days. The short study never saw that. The gap between Cpk and Ppk named the problem exactly: not an incapable process, an uncontrolled one, and the fix was SPC and humidity control rather than a redesign of the seal.
Common mistakes
- Quoting Cpk from a short study as if it described long-term performance. A two-hour Cpk says nothing about between-shift drift.
- Ignoring the Cpk-minus-Ppk gap, which is precisely the long-term instability the process is hiding.
- Computing either index on an out-of-control process. Capability numbers are only meaningful once the process is stable; on an unstable process they are not predictive.
- Confusing capability (does the spread fit the spec) with control (is the process stable). A process can be capable and out of control, or in control and incapable.
- Reporting Cp/Pp (spread only) without Cpk/Ppk (spread and centering), hiding a process that fits the spec width but sits off-center.
Both indices, and the gap that diagnoses drift
Niobia computes Cpk from within-subgroup variation and Ppk from the overall long-term spread on the same characteristic, and reports them together so the gap between them is visible. A close pair confirms a stable, capable process; a healthy Cpk with a lagging Ppk points directly at between-shift or between-day drift, which it ties back to the control charts and EWMA trends that show when and how the process wandered. Because it checks process stability first, the indices it reports are the meaningful, in-control kind rather than numbers computed on a moving target.
Frequently asked
What is the actual difference between Cpk and Ppk?
The sigma in the denominator. Cpk uses short-term, within-subgroup variation (the process at its best); Ppk uses overall, long-term variation (the process as it really ran). Same formula otherwise. The gap between them is the long-term drift a short-term study cannot see.
My Cpk is great but I still make out-of-spec parts. Why?
Almost always between-subgroup drift. A short-term Cpk describes moment-to-moment capability; if the mean shifts between shifts, days, or lots, the long-term Ppk is lower and that is what produces the escapes. Compute Ppk over a long window and the gap will show it.
Do I need the process in control before these numbers mean anything?
Yes. Capability and performance indices assume a stable process; computed on an out-of-control process they are not predictive of future output. Establish control first with charts, then the Cpk/Ppk pair becomes meaningful.