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

USL | Upper specification limit |

LSL | Lower specification limit |

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

Within-subgroup standard deviation |

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

where ν is calculated based on the method used to estimate σ^{2}_{within}:

- Pooled standard deviation: ν = Σ (n
_{i}- 1) - Average moving range and Median moving range: ν ≈ k – Rspan + 1
- Square root of MSSD: ν = k - 1
- Rbar: ν = 0.9 k (n - 1)
- Sbar: ν = f
_{n}k (n - 1), where f_{n}is the adjustment factor that varies with n, as shown in the following table.

n | f_{n} |
---|---|

2 | 0.88 |

3 | 0.92 |

4 | 0.94 |

5 | 0.95 |

6, 7 | 0.96 |

8, 9 | 0.97 |

10-17 | 0.98 |

18-64 | 0.99 |

65- | 1.00 |

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 |

σ^{2}_{within} | Within-subgroup variance |

n_{i} | The i^{th} subgroup size |

k | Number of samples |

Rspan | Length of the moving range |

n | Average sample size (Σ n_{i} / k). |

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) |

Within-subgroup 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) |

Within-subgroup standard deviation |

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

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

N | The total number of observations |

α | Alpha for the confidence level |

v | The degrees of freedom based on the method used to estimate σ^{2}_{within} (for information on the calculation of v, see the section on Cp confidence interval bounds) |

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 |

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 |

Within-subgroup standard deviation | |

Average of the observations | |

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