QM Bench

4 sigma: DPMO, yield and Cpk

By the Six Sigma convention a 4 sigma process produces about 6,210 defects per million opportunities in the long term, which corresponds to Cpk 1.33 short term.
MeasureValue
DPMO long term (1.5 σ shift)6,210
Yield long term99.37903 %
PPM without shift (one side)31.7
Equivalent Cpk (short term)1.33
Equivalent Ppk (long term)0.83

Where the numbers come from

The sigma level is the number of standard deviations between the process mean and the nearest specification limit, measured on short-term data. Six Sigma practice assumes the mean drifts by up to 1.5 σ over time, so the long-term defect rate is calculated at 4 − 1.5 = 2.5 σ. Automotive capability studies usually report Cpk and Ppk without this shift; see Cpk, PPM and sigma level explained.

Other sigma levels

3.5 sigma4.5 sigma

Frequently asked questions

How many defects is 4 sigma?

6,210 DPMO long term, assuming the usual 1.5 sigma shift of the mean. Without that shift the one-sided defect rate is 31.7 PPM.

What Cpk is 4 sigma?

Cpk = sigma level / 3 = 1.33 short term; the long-term Ppk after the 1.5 sigma shift is 0.83.

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