Select the method or formula of your choice.

- Common notation and rules for Gage R&R confidence intervals
- Repeatability variance component confidence interval
- Reproducibility (or Operator) variance component confidence interval
- Operator variance component confidence interval
- Interaction variance component confidence interval
- Total gage variance component confidence interval
- Part-to-part variance component confidence interval
- Total variance component confidence interval

For all variance components, lower and upper bounds for variance components must not be negative values. If the bounds calculated using the formulas are negative, then they are set to zero.

For all ratios between 0 and 1, lower and upper bounds should also be between 0 and 1. If the bounds are outside the range, they are set to 0 or 1 accordingly.

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

F_{α}(n_{q}, n_{γ}) | the α *100 percentile of the F distribution with n_{q } and n_{γ} degrees of freedom |

J | the number of operators |

I | the number of parts |

K | the number of replicates |

For degrees of freedom:

Parts: n_{1}=I–1

Operators: n_{2}=J–1

Part Operator Interaction: n_{3}=(I–1)(J–1)

Replicates: n_{4}=IJ(K–1)

MSPart = S_{1}^{2}

MSOperator = S_{2}^{2}

MSPart*Operator = S_{3}^{2}

MSReplicates = S_{4}^{2}

Minitab calculates the lower and upper bounds for an exact (1 – α) *100% confidence interval. To calculate the one-sided confidence bounds, replace α/2 with α in H and G.

- With operator
- Without operator
- Without interaction term

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

J | the number of operators |

I | the number of parts |

K | the number of replicates |

Minitab uses the modified large-sample (MLS) method to calculate the lower and upper bounds for an approximate (1 – α) *100% confidence interval. To calculate the one-sided confidence bounds, replace α/2 with α in H and G.

- With interaction term
- Without interaction term

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

J | the number of operators |

I | the number of parts |

K | the number of replicates |

Minitab uses the modified large-sample (MLS) method to calculate the lower and upper bounds for an approximate (1–α) *100% confidence interval. To calculate the one-sided confidence bounds, replace α/2 with α in H and G.

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

J | the number of operators |

I | the number of parts |

K | the number of replicates |

Minitab uses the modified large-sample (MLS) method to calculate the lower and upper bounds for an approximate (1 – α) *100% confidence interval. To calculate the one-sided confidence bounds, replace α/2 with α in H and G.

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

J | the number of operators |

I | the number of parts |

K | the number of replicates |

Minitab uses the modified large-sample (MLS) method to calculate the lower and upper bounds for an approximate (1 – α) *100% confidence interval. To calculate the one-sided confidence bounds, replace α/2 with α in H and G.

The lower and upper bounds for an exact (1 – α) *100% confidence interval are:

Minitab uses the modified large-sample (MLS) method, the lower and upper bounds for an approximate (1 – α) *100% confidence interval. To calculate the one-sided confidence bounds, replace α/2 with α in H and G.

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

J | the number of operators |

I | the number of parts |

K | the number of replicates |

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

J | the number of operators |

I | the number of parts |

K | the number of replicates |

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

the α *100 percentile of the chi-square distribution with n_{q }degrees of freedom | |

J | the number of operators |

I | the number of parts |

K | the number of replicates |