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2P-Weibull MLE Solution for Multiple Right Censored Data
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This example compares the calculation for a 2-parameter Weibull MLE solution with likelihood ratio bound for right censored data.
Reference Case
The data 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] = 2.035.
- The B10 life [math]\displaystyle{ t_{0.1} \,\! }[/math] = 3903. Its 95% 2-sided likelihood ratio bounds are [2093, 22, 144].
Results in Weibull++
- The B10 life [math]\displaystyle{ t_{0.1} \,\! }[/math] with 95% 2-sided likelihood ratio bounds are: