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.

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


 * $$\hat{\theta}=\frac{TTT}{r}\ \ and\ \ se_{\hat{\theta}} = \frac{\hat{\theta}}{\sqrt{r}}\,\!$$

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


 * $$\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}\,\!$$

So the variance of $$ \hat{\theta}\,\! $$ is 6567.04