For exact data, every solution, , of the following system of equations maximizes the likelihood.

where:

The standard errors are the standard deviations of the estimate of the parameter. The standard errors are calculated as the square root of the appropriate diagonal element of the inverse of the Fisher information matrix.

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

Y_{i} | retirement time for the i^{th} system |

T_{ij} | j^{th} failure time for the i^{th} system |

n_{i} | number of events for the i^{th} system |

N | number of systems |

For interval data, the maximum likelihood estimates, , satisfy the following equations:

The standard errors are the standard deviations of the estimate of the parameter. The standard errors are calculated as the square root of the appropriate diagonal element of the inverse of the Fisher information matrix.

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

Y_{i} | retirement time for the i^{th} system |

t_{ij} | interval endpoints for the i^{th} system |

k_{i} | number of failures for the i^{th} system |

N_{ij} | number of failures in an interval |

N | total number of systems (in each growth curve) |

where:

The standard error for is:

where
with m_{i} = n_{i} - 1 if Y_{i} = T_{ini} or m_{i} = n_{i} otherwise

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

Y_{i} | retirement time for the i^{th} system |

T_{ij} | j^{th} failure time for the i^{th} system |

n_{i} | number of events for the i^{th} system |

N | total number of systems (in each growth curve) |

where

X_{ij} = logT_{ij}

Y_{ij} = log[T_{ij} ^{-1}N_{i}(T_{ij})]

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

N_{i}(T_{ij}) | number of failures in the interval (0, T_{ij}] |