Lognormal MLE Solution with Right Censored Data
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This example validates the calculations for the Lognormal MLE solution with Fisher matrix bound for right censored data in Weibull++ standard folios.
Reference Case
The data set on page 199 of the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998 is used.
Data
| Number in State | State F or S | Time to Failure |
|---|---|---|
| 1 | F | 252 |
| 1 | F | 315 |
| 1 | F | 369 |
| 1 | F | 403 |
| 1 | F | 474 |
| 15 | S | 500 |
Result
- The MLE solution is
.
- The variance and covariance matrix is
Results in Weibull++
- The following picture shows the MLE solution and the variance/covariance matrix:
- The Fisher matrix bound for parameters are:
- For Ln-mu (using normal approximation of Eqn. 8.7 on page 187):
- For a confidence level of 0.95, it is:
- For Ln-Std (using log-normal approximation of Eqn. 8.8 on page 188):
- For confidence level of 0.95, it is:
- The following picture shows the results in Weibull++:
