QM Bench

1 sigma: DPMO, yield and Cpk

By the Six Sigma convention a 1 sigma process produces about 691,462 defects per million opportunities in the long term, which corresponds to Cpk 0.33 short term.
MeasureValue
DPMO long term (1.5 σ shift)691,462
Yield long term30.85375 %
PPM without shift (one side)158,655
Equivalent Cpk (short term)0.33
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 1 − 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 sigma

Frequently asked questions

How many defects is 1 sigma?

691,462 DPMO long term, assuming the usual 1.5 sigma shift of the mean. Without that shift the one-sided defect rate is 158,655 PPM.

What Cpk is 1 sigma?

Cpk = sigma level / 3 = 0.33 short term; the long-term Ppk after the 1.5 sigma shift is -0.17.

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