Select the method or formula of your choice.

Bias is the difference between the part's reference value and the operator's measurements of the part.

Average bias for each part:

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

z_{i,j} | j^{th} measurement of the i^{th} part |

ref_{i} | reference value of the i^{th} part |

m_{i} | number of replicates of the i^{th} part |

%Bias is bias expressed as a percentage of the overall process variation.

%Bias = 100 * (|Average Bias| / Process Variation)

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

z_{i,j} | j^{th} measurement of the i^{th} part |

ref_{i} | reference value of the i^{th} part |

m_{i} | number of replicates of the i^{th} part |

Use the p-values to test whether bias = 0 at each reference value, and whether the average bias =0.

The p-value is defined as the area under the sampling distribution to the right of the + |test statistic| and the area under the sampling distribution to the left of the - |test statistic|. The p-value in the output is obtained from using the t-distribution with γ df and the t-statistic.

Minitab provides specific t-statistic calculations for the sample range method and for the sample standard deviation method.

Minitab uses either the sample range (default) or sample standard deviation to estimate repeatability standard deviation. Repeatability standard deviation is used to calculate the t-value, which leads to the calculation of the p-value to test bias = 0 for all reference values and for each reference.

For the sample range method, when each distinct reference value corresponds to a unique part, the repeatability standard deviation:

When more than one part has the same reference value, the repeatability standard deviation:

The t-statistic for testing bias is:

The degrees of freedom (γ) is obtained from a table in the AIAG manual^{1}. Minitab uses the t distribution with γ df and the t-value to calculate the p-value.

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

X_{i} | the bias of the i^{th} measurement for a part |

d_{2} | a value from a table^{1}, with sample size = n |

average range |

Minitab uses either the sample range (default) or sample standard deviation to estimate repeatability standard deviation. Repeatability standard deviation is used to calculate the t-value, which leads to the calculation of the p-value to test bias = 0.

For the sample standard deviation method, when one reference value corresponds to a single part, the repeatability standard deviation:

The t-statistic for testing bias is:

The degrees of freedom are n - 1. The p-value in the output is obtained from the t-distribution using the t-value and the degrees of freedom.

When more than one part has the same reference value, the repeatability standard deviation is the pooled sample standard deviation s across the parts with the same reference value:

The t-statistic for testing bias is:

The degrees of freedom are (n_{1}- 1) + ... + (n_{g} - 1). The p-value in the output is obtained from the t-distribution using the t-value and the degrees of freedom.

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

x | i^{th} measurement of the part |

average measurement for the part | |

n | sample size |

S_{1} | the sample standard deviation for part 1 with n_{1} measurements |

S_{g} | the sample standard deviation for part g with n_{g} measurements |