QM Bench

2 sigma: DPMO, yield and Cpk

By the Six Sigma convention a 2 sigma process produces about 308,538 defects per million opportunities in the long term, which corresponds to Cpk 0.67 short term.
MeasureValue
DPMO long term (1.5 σ shift)308,538
Yield long term69.14625 %
PPM without shift (one side)22,750
Equivalent Cpk (short term)0.67
Equivalent Ppk (long term)0.17

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 2 − 1.5 = 0.5 σ. Automotive capability studies usually report Cpk and Ppk without this shift; see Cpk, PPM and sigma level explained.

Other sigma levels

1.5 sigma2.5 sigma

Frequently asked questions

How many defects is 2 sigma?

308,538 DPMO long term, assuming the usual 1.5 sigma shift of the mean. Without that shift the one-sided defect rate is 22,750 PPM.

What Cpk is 2 sigma?

Cpk = sigma level / 3 = 0.67 short term; the long-term Ppk after the 1.5 sigma shift is 0.17.

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