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

USL | Upper specification limit |

LSL | Lower specification limit |

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

Overall standard deviation |

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

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 | The degrees of freedom (Σn_{i}– 1) |

n_{i} |
The number of observations in the ith subgroup |

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

Process mean (estimated from the sample data or a historical value) | |

LSL | Lower specification limit |

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

Overall standard deviation |

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

USL | Upper specification limit |

Process mean (estimated from the sample data or a historical value) | |

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

Overall standard deviation |

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

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

N | The total number of observations |

α | Alpha for the confidence level |

v | The degrees of freedom (Σn_{i} – 1 or N – 1) |

n_{i} | The number of observations in the i^{th} subgroup |

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

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

Cpm is available only when a target is specified. Minitab calculates Cpm based on known values of LSL, USL, and T.

Known value | Cpm |
---|---|

LSL and USL only | * |

LSL, USL, and T = m | |

LSL, USL, and T ≠ m | |

USL and T only | |

LSL and T only | |

Either LSL or USL only | * |

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

* | Missing value |

USL | Upper specification limit |

LSL | Lower specification limit |

m | Midpoint between USL and LSL |

T | Target value |

X_{ij} | j^{th} observation in the i^{th} subgroup |

n_{i} | Number of observations in the i^{th} subgroup |

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

Minitab calculates the (1 – α) 100% two-sided confidence interval for Cpm as follows:

The (1 – α) 100% lower confidence bound for Cpm is calculated as follows:

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

α quantile of the chi-square distribution with ν degrees of freedom | |

Degrees of freedom, defined as N ((1 + a^{2}) ^{2} / (1 + 2a^{2})) | |

a | (Mean – Target)/ |

α | Alpha for the confidence level |

N | Total number of observations |