2P-Weibull MLE Solution for Multiple Right Censored Data

From ReliaWiki
Jump to navigation Jump to search
Weibull Reference Examples Banner.png


2P-Weibull MLE Solution for Multiple Right Censored Data

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]\hat{\beta}\,\![/math] is 2.035.
  • The B10 life [math]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++:
2PW MLE right censored.png


  • The B10 life [math]t_{0.1} \,\![/math] with 95% 2-sided likelihood ratio bounds are shown next:
2PW MLE right censored QCP.png