Pp is the overall process performance index. It compares the specification window to the total process variation measured using the overall (population) standard deviation. Pp is to Ppk what Cp is to Cpk: it measures spread without accounting for centering.
The Formula
Pp = (USL - LSL) / 6σo
Where:
- USL is the upper specification limit
- LSL is the lower specification limit
- σo is the overall (population) standard deviation
The structure is identical to Cp. The only difference is σo (overall) instead of σ (within-subgroup). This means Pp captures all variation: within-batch, between-batch, between-shift, and between-operator.
Pp vs Cp
Cp uses the within-subgroup σ and answers: "If we only look at short-term variation, does the spec window have room?" Pp uses the overall σo and answers: "Over the full production run, does the spec window have room?"
| Index | Standard Deviation | Time Horizon | Question |
|---|---|---|---|
| Cp | Within-subgroup σ | Short-term | Can this process fit within specs under controlled conditions? |
| Pp | Overall σo | Long-term | Does this process fit within specs over real production? |
When Pp is close to Cp, the process is stable over time. When Pp is noticeably lower than Cp, there's hidden variation between production runs that inflates the overall spread.
What Pp Values Mean
| Pp | Interpretation |
|---|---|
| < 1.0 | Long-term variation exceeds spec window. Process can't consistently meet specs over time. |
| 1.0 | Long-term variation exactly fills the spec window. |
| 1.33 | Process uses 75% of the spec window long-term. Standard target. |
| > 1.67 | Process has significant long-term margin. |
Reading Pp in TofuPilot
Open the Process Control page, select a numeric measurement, and switch to the Capability tab. Pp appears in the second (teal) KPI row alongside Ppk, Ppl, and Ppu. The first (purple) row shows the Cp family.
If Pp is lower than Cp, your process has more variation over time than within individual batches. That points to batch-level or environmental sources of variation worth investigating.
Like all indices on the Capability tab, click Pp to toggle its trend line on the daily chart. Watching Pp over weeks helps you see whether long-term variation is growing or shrinking.
Pp Requires Both Spec Limits
Like Cp, Pp needs both USL and LSL. For one-sided specifications, TofuPilot computes Ppu (upper only) or Ppl (lower only) instead.
When Pp Matters Most
Pp is particularly useful during initial process validation (PPAP, process qualification). It tells you whether the process can sustain capability over a meaningful production window, not just during an optimized short run. Automotive PPAP studies typically require Pp >= 1.67 before granting production approval.