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 and the standard error of are given on page 193.
-
- and
where is given,
is the time for the
ith observation, r is the number of failures. Appling this equation, we get the following results:
-
- and
Results in Weibull++
The variance of eta is 6.324612E+06. The standard deviation is 2514.88.