Competing Failure Modes

This example validates the competing failure mode calculations in Weibull++ standard folios.

Reference Case

The data set is from Table 15.1 on page 383 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.

Data

State F/S	Time to F/S	Failure Mode
F	275	w
F	13	s
F	147	w
F	23	s
F	181	w
F	30	s
F	65	s
F	10	s
S	300
F	173	s
F	106	s
S	300
S	300
F	212	w
S	300
S	300
S	300
F	2	s
F	261	s
F	293	w
F	88	s
F	247	s
F	28	s
F	143	s
S	300
F	23	s
S	300
F	80	s
F	245	w
F	266	w

Result

In the book, parameters and are used for the Weibull distribution. They are defined by and . The results are:

• For failure mode s, the log-likelihood value is -101.36.
• For failure mode s, = 6.11 and its approximated 95% confidence interval are [5.27, 6.95].
• For failure mode s, = 1.49 and its approximated 95% confidence interval are [0.94, 2.36].
• For failure mode w, the log-likelihood value is -47.16.
• For failure mode w, = 5.83 and its approximated 95% confidence interval are [5.62, 6.04].
• For failure mode w, = 0.23 and its approximated 95% confidence interval are [0.12, 0.44].

Results in Weibull++

• The following picture shows the ML estimates and the variance covariance matrix for each failure mode.

• The following picture shows the 95% confidence intervals for the parameters of each failure mode.

• In terms of and , the results are:

• For failure mode s, = 6.11 and its approximated 95% confidence interval are [5.27, 6.95].
• For failure mode s, = 1.49 and its approximated 95% confidence interval are [0.94, 2.36].
• For failure mode w, = 5.83 and its approximated 95% confidence interval are [5.62, 6.04].
• For failure mode w, = 0.23 and its approximated 95% confidence interval are [0.12, 0.44].

The above results are exactly the same as the results in the book.