If you specify the planning values for both μ and σ (θ and β for the Weibull model), then Minitab calculates the percentile or the reliability.

- The planning value for the pth percentile is calculated as follows:
- for location-scale models (normal, logistic and extreme value)
- for log-location-scale models (Weibull, lognormal, loglogistic)

- The planning value for reliability at a given time is calculated as follows:
- for location-scale models (normal, logistic, extreme value)
- for log-location-scale models (Weibull, lognormal, loglogistic)

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

μ | mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

σ | scale parameter |

θ | scale parameter for Weibull |

β | shape parameter for Weibull |

t | time |

t_{p,plan} | planning value for the pth percentile at time t |

R_{plan}(t) | planning value for reliability at time t |

Φ | CDF for the corresponding distribution |

Φ^{-1 } | inverse CDF for the corresponding distribution |

If you specify the planning values for β (or σ) and a percentile t_{p}_{0}, then Minitab calculates the planning value for μ as follows:

- For location-scale models (normal, logistic and extreme value)
- For log-location-scale models (Weibull, lognormal and loglogistic)

To obtain the planning value for the percentile or the reliability, use the calculations for when two parameters are specified. For more information, see the section "Two distributional parameters specified".

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

μ | mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

μ_{plan} | planning value for mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

σ | scale parameter |

σ_{plan} | planning value for scale parameter |

β | shape parameter for Weibull |

t | time |

t_{p} | percentile at time t |

Φ^{-1 } | inverse CDF for the corresponding distribution |

If you specify the planning values for μ (or θ) and a percentile t_{p}_{0} then Minitab calculates the planning value for σ as follows:

- For location-scale models (normal, logistic and extreme value)
- For log-location-scale models (Weibull, lognormal and loglogistic)

To obtain the planning value for the percentile or the reliability, use the calculations for when two parameters are specified. For more information, see the section "Two distributional parameters specified".

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

μ | mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

μ_{plan} | planning value for mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

σ | scale parameter |

σ_{plan} | planning value for scale parameter |

β | shape parameter for Weibull |

t | time |

t_{p} | percentile at time t |

Φ^{-1 } | inverse CDF for the corresponding distribution |

If you specify the planning values for two percentiles, then Minitab calculates the planning values for both μ and σ.

- The planning value for μ is calculated as follows:
- For location-scale models (normal, logistic and extreme value)
- For log-location-scale models (Weibull, lognormal, loglogistic)

- The planning value for σ is calculated as follows:
- For location-scale models (normal, logistic, extreme value)
- For log-location-scale models (Weibull, lognormal, loglogistic)

To obtain the planning value for the percentile or the reliability, use the calculations for when two parameters are specified. For more information, see the section "Two distributional parameters specified".

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

μ | mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

μ_{plan} | planning value for mean (normal, logistic), location (smallest extreme value), or log-location (lognormal, loglogistic) |

σ | scale parameter |

σ_{plan} | planning value for scale parameter |

β | shape parameter for Weibull |

t | time |

t_{p} | percentile at time t |

Φ^{-1 } | inverse CDF for the corresponding distribution |