The question
A continued process verification report shows a capability index (Ppk) for monomer purity comfortably above target across 40 batches, and concludes the process is capable. Is it?
The analysis
| Measure | Value |
|---|---|
| Ppk over all 40 batches, as reported | 1.62 |
| Trend in monomer per batch (regression slope) | -0.039 % per batch, p < 0.001 |
| First run rule signal (8 consecutive below center line) | batch 22 |
| Ppk, most recent 12 batches (looks even better: a short window hides the trend) | 2.13 |
| Batch where the trend brings the 3-sigma band to the lower spec | about 63 |
A capability index assumes a stable process: one mean and one spread. This process is drifting down. Ppk over all 40 batches averages early and late batches into one number that no single batch resembles, and a shorter recent window looks even better because it is too short to show the trend. Either way, the index describes the past, not where the process is heading.
What to do
- Open an investigation on the trend signal, not on the capability number.
- Report capability only for a period that passes control-chart run rules, and state that period.
- Use the projected crossing point to set how urgently the root cause needs to be found, and trend the mean itself, not just capability.
How it was done
Synthetic monomer results for 40 batches with a slow downward drift. Individuals chart with limits from batches 1 to 20 (moving-range sigma), Western Electric run rule of eight consecutive points on one side, linear regression for the trend, and Ppk computed as (mean minus LSL) / (3 x overall SD). Download the data (CSV).