The probability density function (pdf) and cumulative distribution function (cdf) for each reliability distribution are as follows:

- cdf

- cdf

- cdf

- cdf

- cdf

- cdf

- cdf

- cdf

- cdf

- cdf

- cdf

For more information on distribution parameters, see the section "Parameter estimates".

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

μ | location parameter |

σ | scale parameter (Weibull and 3-parameter Weibull) |

θ | scale parameter (smallest extreme value, exponential, and 2-parameter exponential) |

α | scale parameter (other distributions) |

β | shape parameter |

λ | threshold parameter |

The hazard function provides a measure of the likelihood of failure as a function of how long a unit has survived (the instantaneous failure rate at a particular time, *t*).

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

f(t) | pdf of the chosen distribution |

F(t) | cdf of the chosen distribution |

When data follow a log-based distributions (Weibull, exponential, lognormal, loglogistic), sometimes calculations are simpler by first taking the log of your data and fitting the corresponding related distribution.

If your data follow this distribution... | The log of your data will follow this distribution... |
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Weibull, exponential | Smallest extreme value |

Lognormal | Normal |

Loglogistic | Logistic |