Term | Description |
---|---|

USL | Upper specification limit |

LSL | Lower specification limit |

Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |

Between/within standard deviation |

The (1 -α) 100% confidence interval for Cp is calculated as follows:

where ν is approximated by

and

Term | Description |
---|---|

χ^{2}_{α}_{,}_{ν} | The α percentile of the chi-square distribution with ν degrees of freedom |

α | Alpha for the confidence level |

ν | Degrees of freedom |

Y_{ij} | The jth observation in the ith subgroup |

The ith subgroup average | |

The average across all subgroups | |

I | The number of subgroups |

n_{i} | The ith subgroup size |

Term | Description |
---|---|

Average of the observations | |

LSL | Lower specification limit |

Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |

Between/within standard deviation |

Term | Description |
---|---|

USL | Upper specification limit |

Average of the observations | |

Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |

Between/within standard deviation |

The (1 -α) 100% confidence interval for Cpk is calculated as follows:

If the sigma tolerance value, say k, in the input is not the default 6, then 9 in the formula should be replaced by (k/2)**2.

Term | Description |
---|---|

N | The total number of observations |

α | Alpha for the confidence level |

v | The degrees of freedom. For information on the calculation of ν, see the topic on the Cp confidence interval for between/within capability analysis. |

Z_{1}-_{α}_{/2} | The 1-α/2 percentile from the standard normal distribution |

Minitab calculates CCpk based on known values of LSL, USL, and T.

Known value | CCpk |
---|---|

USL only | |

LSL only | |

LSL and USL |

where:

Term | Description |
---|---|

Estimator for the population mean | |

USL | Upper specification limit |

LSL | Lower specification limit |

Between/within standard deviation | |

Average of the observations | |

Toler | Multiplier of the sigma tolerance (Minitab uses 6 as the default value) |