# 1P-Exponential MLE Solution with Right Censored Data: Difference between revisions

 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.

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

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

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

{\displaystyle {\begin{aligned}{\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{aligned}}\,\!}

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

Results in Weibull++