1P-Weibull MLE Solution for Multiple Right Censored Data

This example validates the calculations for a 1-parameter Weibull MLE solution with right censored data in Weibull++ standard folios.

The data set in Table C.5 on page 633 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998 is used.

The formulas for calculating the ML $$\eta\,\!$$ and the standard error of $$\eta\,\!$$ are given on page 193.


 * $$\hat{\eta}=\left (\frac{\sum^{n}_{i=1}t^{\beta}_{i}}{r} \right)^{\frac{1}{\beta}}\,\!$$  and    $$se_{\hat{\eta}}=\frac{\hat{\eta}}{\beta}\sqrt{\frac{1}{r}}\,\!$$

where $$\beta\,\!$$ is given, $$t_{i}\,\!$$ is the time for the ith observation, r is the number of failures. Appling this equation, we get the following results:


 * $$\hat{\eta}=\left (\frac{\sum^{n}_{i=1}t^{\beta}_{i}}{r} \right)^{\frac{1}{\beta}} = 12320.33\,\!$$   and   $$se_{\hat{\eta}}=\frac{\hat{\eta}}{\beta}\sqrt{\frac{1}{r}} = 2514.88\,\!$$

The variance of eta is 6.324612E+06. The standard deviation is 2514.88.