Ppk is the process performance index. It measures the same thing as Cpk (how well your process fits within spec limits) but uses the overall standard deviation instead of the sample standard deviation. This makes Ppk a long-term metric that captures all sources of variation: batch-to-batch, shift-to-shift, operator-to-operator, and environmental.
The Formula
Ppk = min((USL - X̄) / 3σo, (X̄ - LSL) / 3σo)
Where:
- USL is the upper specification limit
- LSL is the lower specification limit
- X̄ is the process mean
- σo is the overall standard deviation (n divisor)
The only difference from Cpk is the standard deviation. Cpk uses σ (sample, n-1 divisor). Ppk uses σo (overall, n divisor).
Sample vs Overall Standard Deviation
This distinction matters. The sample σ (n-1 divisor) provides an unbiased estimate of process variation and is used for short-term capability. The overall σo (n divisor) captures the total observed variation across the full dataset, including all between-run sources.
| Statistic | Divisor | Captures |
|---|---|---|
| Sample σ | n-1 | Short-term variation: instrument noise, part-to-part within a batch |
| Overall σo | n | All variation: batch shifts, operator differences, temperature changes, lot variation |
Overall σo is always equal to or larger than sample σ. So Ppk is always equal to or lower than Cpk.
What the Gap Between Cpk and Ppk Tells You
When Cpk and Ppk are close, your process is consistent over time. The variation you see in a single batch is representative of the whole production run.
When Cpk is significantly higher than Ppk, something is changing between batches. Your process looks capable in any given short window, but over days or weeks, extra variation appears.
| Cpk | Ppk | Diagnosis |
|---|---|---|
| 1.5 | 1.4 | Process is stable. Short-term and long-term variation are similar. |
| 1.5 | 0.9 | Hidden variation between batches. Investigate lot changes, operator differences, or environmental shifts. |
| 0.8 | 0.8 | Process isn't capable even short-term. Fix fundamental variation first. |
When to Use Ppk vs Cpk
Use Cpk to assess inherent process capability under controlled conditions. Use Ppk to assess real-world performance over time.
PPAP (Production Part Approval Process) in automotive typically requires Ppk >= 1.67 for initial process studies. Ongoing production monitoring uses Cpk >= 1.33.
Reading Ppk in TofuPilot
Open the Process Control page, select a numeric measurement, and switch to the Capability tab. The second KPI row shows the Pp family: Ppk, Pp, Ppl, and Ppu in teal. The first row shows the Cp family in purple.
Compare the two rows at a glance. If the teal values are noticeably lower than the purple ones, you have between-batch variation to investigate.
Click any index to toggle its line on the daily trend chart. Tracking Ppk alongside Cpk over time reveals when long-term variation starts growing.
Common Pitfalls
Small datasets blur the distinction. With fewer than 50 data points from a single batch, σ and σo converge. The Cpk/Ppk gap only becomes meaningful with data spanning multiple batches, shifts, or days.
Don't compare Ppk across different time windows without context. Ppk over 7 days will differ from Ppk over 90 days because more sources of variation enter the calculation.