Var (MLE) and Cov (μ,σ) are the variances and covariances of the MLEs of μ, σ, α, and β taken from the appropriate element of the inverse of the Fisher information matrix.

The sample size needed to estimate the percentile, t_{p}, is calculated as follows:

- For a two-sided confidence interval:
- For a one-sided confidence interval:

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

t_{p} | percentile |

MLE* | maximum likelihood estimate (MLE) of t_{p} |

Avar(MLE*) | asymptotic variance of the MLE at design (or use) stress level |

Φ^{-1}_{nor} | inverse CDF of the normal distribution |

D_{T} | distance between the estimate and the upper or lower bound of the (1 – α)100% confidence interval, based on the bound that you specified for the analysis |

- For a two-sided confidence interval:
- For a one-sided confidence interval: where

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

t_{p} | percentile |

MLE* | maximum likelihood estimate (MLE) of ln (t_{p}) |

Avar(MLE*) | asymptotic variance of the MLE at design (or use) stress level |

Φ^{-1}_{nor} | inverse CDF of the normal distribution |

D_{T} | distance between the estimate and the upper or lower bound of the (1 – α)100% confidence interval, based on the bound that you specified for the analysis |

The MLE of the standardized time when you estimate reliability is calculated as follows:

- For a two-sided confidence interval:
- For a one-sided confidence interval:

where

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

MLE* | standardized time |

Avar(MLE*) | asymptotic variance of the MLE |

Φ^{-1}_{nor} | inverse CDF of the normal distribution |

D_{T} | distance between the estimate and the upper (or lower) bound of the (1 – α)100% confidence interval |