Sigma |
DPMO |
Yield |
Cpk |

1.5 | 500,000 | 50% | 0.50 |

3.00 | 66,800 | 93.320% | 1.00 |

3.50 | 22,700 | 97.730% | 1.17 |

4.00 | 6,210 | 99.3790% | 1.33 |

4.50 | 1,350 | 99.8650% | 1.50 |

5.00 | 230 | 99.9770% | 1.67 |

6.00 | 3.4 | 99.99966% | 2.00 |

**Assumptions**

No analysis would be complete without properly noting the assumptions made. In the above table, we have assumed that theÂ standard sigma shift of 1.5Â is appropriate (theÂ calculatorÂ allows you to specify another value), the data is normally distributed, and the process is stable. In addition, the calculations are made with usingÂ one-tail valuesÂ of the normal distribution.

**Discussion**

If you are starting with DPMO, convert it to a decimal value by dividing by 1,000,000. If you multiply that decimal by 100, that is your Yield (%). If you take the decimal and look it up in a standard normal curve (Z table), you can determine the corresponding Z which is the long term Z. To convert to short term Z, which is the Sigma level, use the following formula:

Z(short term) = Z(long term) + 1.5

Then you can determine Cpk using the following formula:

Cpk = Z(short-term) / 3