Cpk and Ppk answer the same question (can my process meet spec?) but over different time horizons. Cpk uses the sample standard deviation and reflects short-term capability. Ppk uses the overall standard deviation and reflects long-term performance. The gap between them tells you whether your process is stable over time.
The Formulas Side by Side
| Index | Formula | Standard Deviation |
|---|---|---|
| Cpk | min((USL - X̄) / 3σ, (X̄ - LSL) / 3σ) | Sample σ (n-1 divisor) |
| Ppk | min((USL - X̄) / 3σo, (X̄ - LSL) / 3σo) | Overall σo (n divisor) |
The formulas are identical except for σ. That one difference changes the meaning.
Sample vs Overall Standard Deviation
The sample σ (n-1 divisor) provides an unbiased estimate of process variation. For individual measurements (one value per unit, which is the typical case in electronics testing), this captures short-term variation under controlled conditions.
The overall σo (n divisor) captures the total observed variation across the full dataset, including all between-run sources: batch-to-batch shifts, operator differences, temperature changes, component lot variation, fixture wear.
Overall σo is always >= sample σ. So Ppk is always <= Cpk. When they're equal, the process is perfectly stable over time. When Ppk is lower, there's hidden variation between production runs.
What the Gap Tells You
| Cpk | Ppk | Gap | Diagnosis |
|---|---|---|---|
| 1.5 | 1.45 | Small | Process is stable. Short-term and long-term variation are similar. No action needed. |
| 1.5 | 1.0 | Large | Process looks capable in any given batch but degrades over time. Investigate what changes between batches. |
| 1.5 | 0.7 | Very large | Significant between-batch variation. Common causes: component lot changes, operator training gaps, environmental shifts. |
| 0.8 | 0.8 | None | Process isn't capable even short-term. Fix fundamental variation before worrying about batch-to-batch stability. |
A large Cpk-Ppk gap is a signal to investigate sources of variation that don't show up within a single batch. Common culprits:
- Component lot variation. A new reel of resistors shifts the circuit's behavior slightly. Each lot is in spec, but the distribution center moves.
- Operator differences. Different fixture handling, different placement pressure, different ambient temperature from body heat near the DUT.
- Environmental changes. Morning vs afternoon temperature, seasonal humidity shifts, facility voltage fluctuations.
- Fixture wear. Pogo pin spring force degrading over thousands of insertions. Still passing, but adding variation.
When to Use Each
| Context | Use | Why |
|---|---|---|
| Ongoing production monitoring | Cpk | You want to know if the process is inherently capable under controlled conditions. |
| PPAP / initial process study | Ppk | Automotive standards require Ppk >= 1.67 to prove real-world performance. |
| Process qualification | Both | Compare them. A large gap means the process isn't ready for unsupervised production. |
| Root cause analysis | Both | If Cpk is fine but Ppk is low, the problem is between batches, not within them. |
Industry Requirements
| Standard | Cpk Requirement | Ppk Requirement |
|---|---|---|
| IATF 16949 (automotive) | >= 1.33 ongoing | >= 1.67 initial study |
| AS9100 (aerospace) | >= 1.33 production | >= 1.33 qualification |
| ISO 13485 (medical) | Per product risk | Per product risk |
| General electronics | >= 1.33 typical | >= 1.33 typical |
Comparing Cpk and Ppk in TofuPilot
Open the Process Control page, select a numeric measurement, and switch to the Capability tab. The purple row shows Cpk (with Cp, Cpl, Cpu). The teal row shows Ppk (with Pp, Ppl, Ppu). You can compare both families at a glance.
Click any index to toggle it on the daily trend chart. Plotting Cpk and Ppk together over time is the clearest way to see whether the gap is growing, shrinking, or stable.
If you notice Ppk trending downward while Cpk stays flat, something external to the process is introducing variation. Filter by station, operator, or batch in the sidebar to isolate the source.
Quick Decision Guide
Cpk high, Ppk high: Process is capable and stable. Monitor and maintain.
Cpk high, Ppk low: Process is capable within batches but unstable over time. Investigate between-batch variation.
Cpk low, Ppk low: Process isn't capable. Reduce variation first (σ), then worry about stability.
Cpk low, Ppk high: Unusual. Possible data issue or very small dataset. Verify your data filters.