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2P-Weibull MLE Solution for Multiple Right Censored Data
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This example validates the calculations for a 2-parameter Weibull MLE solution with likelihood ratio bound for right censored data in Weibull++ standard folios.
Reference Case
The data set in Table C.5 on page 633 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
|
| 288 |
S |
50
|
| 148 |
S |
150
|
| 1 |
F |
230
|
| 124 |
S |
250
|
| 1 |
F |
334
|
| 111 |
S |
350
|
| 1 |
F |
423
|
| 106 |
S |
450
|
| 99 |
S |
550
|
| 110 |
S |
650
|
| 114 |
S |
750
|
| 119 |
S |
850
|
| 127 |
S |
950
|
| 1 |
F |
990
|
| 1 |
F |
1009
|
| 123 |
S |
1050
|
| 93 |
S |
1150
|
| 47 |
S |
1250
|
| 41 |
S |
1350
|
| 27 |
S |
1450
|
| 1 |
F |
1510
|
| 11 |
S |
1550
|
| 6 |
S |
1650
|
| 1 |
S |
1850
|
| 2 |
S |
2050
|
Result
The results are given on page 193 in Example 8.16.
- The MLE solution for [math]\displaystyle{ \hat{\beta}\,\! }[/math] is 2.035.
- The B10 life [math]\displaystyle{ t_{0.1} \,\! }[/math] is 3903. Its 95% 2-sided likelihood ratio bounds are [2093, 22, 144].
Results in Weibull++
- The following picture shows the MLE solutions in Weibull++:
- The B10 life [math]\displaystyle{ t_{0.1} \,\! }[/math] with 95% 2-sided likelihood ratio bounds are shown next:
