Formulas
- Two-sided, centred:
PPM = 2 · Φ(−3 · Cpk) · 10⁶ - One-sided:
PPM = Φ(−3 · Cpk) · 10⁶ - Six Sigma long-term:
DPMO = Φ(−(Z − 1.5)) · 10⁶
These conversions assume a normal distribution. For real data, calculate the expected PPM directly in the process capability study, which also handles non-normal data.
Frequently asked questions
›How many PPM is Cpk 1.33?
For a centred, normally distributed process with two-sided limits, Cpk 1.33 corresponds to about 66 PPM (63 PPM is often quoted for exactly 4 sigma). With one-sided limits it is about 33 PPM.
›Why does 6 sigma mean 3.4 PPM and not 0.002 PPM?
The Six Sigma convention assumes the process mean drifts by 1.5 sigma in the long term. A 6 sigma process then has 4.5 sigma to the nearest limit, which gives 3.4 defects per million. Without the shift, 6 sigma gives about 0.002 PPM.
›Is sigma level the same as Cpk × 3?
The short-term sigma level (Z) is 3 × Cpk. The long-term sigma level subtracts the assumed shift, usually 1.5.