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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.
Reference Case
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.
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 formulas for calculating the ML [math]\displaystyle{ \eta\,\! }[/math] and the standard error of [math]\displaystyle{ \eta\,\! }[/math] are given on page 193.
where [math]\displaystyle{ \beta\,\! }[/math] is given, [math]\displaystyle{ t_{i}\,\! }[/math] is the time for the ith observation, r is the number of failures. Appling this equation, we get the following results:
Results in Weibull++
The variance of eta is 6.324612E+06. The standard deviation is 2514.88.
