Select the method or formula of your choice.

Minitab calculates the adjusted defect counts (*a _{i}*) as follows:

The adjusted counts are then transformed using the following formula:

Then Minitab creates a standard normal probability plot of the transformed counts using the method specified in .

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

d_{i} | defect count for subgroup i |

n_{i} | size of subgroup i |

average subgroup size |

The expected variation is equal to the standard deviation of the transformed counts (*X _{i}*), which is equal to 1.

To calculate the observed variation, Minitab calculates normal scores (*Y,*) for the transformed counts as follows:

where NSCOR is the Normal scores function (available by choosing ).

For the next step, only the middle 50% of the *X _{i}* values are used, along with their corresponding

Minitab fits a least squares regression model with *Y _{i}* as the response and

The observed variation is then 1 / *β*_{1}.

The ratio of observed variation to expected variation is calculated as follows:

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

X_{i} | transformed counts (For more information, see the section "Plotted points".) |

β_{0} | intercept from the least squares regression equation |

β_{1} | slope coefficient from the least squares regression equation |

The upper confidence limit for the ratio is calculated as follows:

where is the mean defect rate, calculated as follows:

For the lower confidence limit for the ratio, Minitab uses a conservative, fixed value of 60%.

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

m | number of subgroups |

average subgroup size | |

d_{i} | defect count for subgroup i |

n_{i} | size of subgroup i |

Minitab compares the ratio of observed variation to expected variation to the 95% upper confidence limit and the 95% lower confidence limit.

- If ratio > upper confidence limit
- If the ratio is greater than the upper confidence limit, then using a traditional U chart with the data may result in an elevated false alarm rate. A Laney U' chart is recommended.
- If ratio < lower confidence limit
- If the ratio is less than the lower confidence limit, then using a traditional U chart with the data may result in control limits that are too wide. A Laney U' chart is recommended.