Ppk brings the average back into the picture. Using the overall mean x̄ and the overall sigma, calculate the upper half (USL − x̄) / 3σ and the lower half (x̄ − LSL) / 3σ, then take the smaller. Ppk tells you how the process actually performed against its nearest limit over the whole study, drift and all.
The gap between Pp and Ppk works exactly like the gap between Cp and Cpk: it measures how far the long-term average sat from the tolerance midpoint. On a moulding press this often points to a nominal that was set conservatively high to avoid short shots, or to a setup sheet that never matched the drawing centre.
Key Concept
Ppk = min[(USL − x̄) / 3σ overall, (x̄ − LSL) / 3σ overall]; the Pp − Ppk gap shows long-term off-centring.
Practical Example
The housing weights over six weeks average x̄ = 42.3 g with overall sigma 0.40 g, so 3σ = 1.20 g. Upper half: (43.5 − 42.3) / 1.20 = 1.2 / 1.20 = 1.00. Lower half: (42.3 − 40.5) / 1.20 = 1.8 / 1.20 = 1.50. Ppk = 1.00. Compared with Pp = 1.25, the gap of 0.25 shows the process ran 0.3 g heavy on average across the study, costing a fifth of the available margin on the upper side.
Standard Procedure
- 1Calculate the overall mean x̄ from all individual readings.
- 2Multiply the overall sigma by 3.
- 3Compute both half-indices and take the smaller as Ppk.
- 4Compare Ppk with Pp; the gap is the centring penalty over the long term.
Lesson Summary
- ✓Ppk is the long-term index that reflects the limit the process actually came closest to.
- ✓Ppk can never exceed Pp, and equals it only when the long-term average sits dead centre.