There are different calculations for the long-term statistics depending on whether you have specified shift or drift (variation expansion) factors for the elements and which gap specifications are given.

Shift and drift factors are used to accommodate unexpected errors or movement over time.

- Drift is a change in the variance over time, while the mean does not exhibit a systematic change.
- Shift is a systematic change in the mean over time. Typically, a shift of 1.5 sigma accommodates unexpected errors or movement over time.

For calculations for short-term statistics, go to Calculations for the gap distribution (short-term statistics) for Allocate Gap Pools.

- One or no gap specification
- Both gap specifications

- One or no gap specification
- Both gap specifications

- One or no gap specification
- Both gap specifications

- One or no gap specification
- Both gap specifications

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

C_{i} | Diametrical correction of the i^{th} element |

D_{i} | Drift factor for the i^{th} element |

N_{i} | Complexity of the i^{th} element |

S_{i} | Shift factor for the i^{th} element |

σ_{i} | Standard deviation of the i^{th} element |

σ_{adj,i} | Adjusted standard deviation of the i^{th} element |

T | Gap targeted value (if not available, T = μ_{Gap,ST}) |

T_{i} | Nominal value of the i^{th} element |

μ_{i} | Mean of the i^{th} element |

μ_{adj,i} | Adjusted mean of the i^{th} element |

V_{i} | Directional vector of the i^{th} element |

w_{i} | Allocation weight for the mean pool or the variance pool, i^{th} element |

Z.Bench_{Gap,LT} | Benchmark Z (long-term) of the gap |

Z.Bench_{Gap,ST} | Benchmark Z (short-term) of the gap |

Z.Bench_{i,LT} | Benchmark Z (long-term) of the i^{th} element |

Z.Bench_{i,ST} | Benchmark Z (short-term) of the i^{th} element |

Z_{P} | Z-value, which gives desired PPM (right tail) for long-term gap distribution |