1P-Weibull MLE Solution for Multiple Right Censored Data

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at Weibull examples and Weibull reference examples.

This example compares the calculation for a 1-parameter Weibull MLE solution with right censored data.

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.

[math]\displaystyle{ \hat{\eta}=\left (\frac{\sum^{n}_{i=1}t^{\beta}_{i}}{r} \right)^{\frac{1}{\beta}}\,\! }[/math] and [math]\displaystyle{ se_{\hat{\eta}}=\frac{\hat{\eta}}{\beta}\sqrt{\frac{1}{r}}\,\! }[/math]

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:

[math]\displaystyle{ \hat{\eta}=\left (\frac{\sum^{n}_{i=1}t^{\beta}_{i}}{r} \right)^{\frac{1}{\beta}} = 12320.33\,\! }[/math] and [math]\displaystyle{ se_{\hat{\eta}}=\frac{\hat{\eta}}{\beta}\sqrt{\frac{1}{r}} = 2514.88\,\! }[/math]

Results in Weibull++

The standard deviation of eta is 6.324612E+06.

1P-Weibull MLE Solution for Multiple Right Censored Data

Navigation menu

Search