# 1P-Exponential MLE Solution with Right Censored Data

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1P-Exponential MLE Solution with Right Censored Data |

This example validates the calculations for the MLE solution and Fisher Matrix bound for a 1-parameter exponential distribution with right censored and complete failure data in Weibull++ standard folios.

Reference Case

The formulas on page 166 in the book *Statistical Methods for Reliability Data* by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.

- [math]\hat{\theta}=\frac{TTT}{r}\ \ and\ \ se_{\hat{\theta}} = \frac{\hat{\theta}}{\sqrt{r}}\,\![/math]

where *TTT *is the total test time and *r* is the number of failures.

Data

Number in State | State F or S | Time to Failure |
---|---|---|

1 | F | 16 |

1 | F | 34 |

1 | F | 53 |

1 | F | 75 |

1 | F | 93 |

1 | F | 120 |

4 | S | 200 |

Result

- [math]\begin{align} \hat{\theta} =& \frac{TTT}{r} = \frac{16+34+53+75+93+120+4\times 200}{6} = \frac{1191}{6} = 198.5 \\ \\ se_{\hat{\theta}} =& \frac{\theta}{\sqrt{r}} = \frac{198.5}{\sqrt{6}} = 81.037 \\ \end{align}\,\![/math]

So the variance of [math] \hat{\theta}\,\! [/math] is 6567.04

Results in Weibull++

- This page was last edited on 28 September 2015, at 16:17.
- Creative Commons Attribution.