I am using WINBUGS to analyze fatigue test
data for welded joints. Each test specimen contains several welds. The test usually
stops when the first weld fails. I am treating the results for the welds that
didn't fail as censored data. I have applied the censoring using the I(,)
construct. The analysis results do NOT look reasonable. It's difficult to
explain why without presenting graphs but, essentially, the predicted fatigue
lives for the welds that didn't fail appear too long when compared with the
lives for the welds that actually failed. I have a couple of questions.
Firstly, is there any description available of the methodology used by WINBUGS
to handle censored test data?
Secondly, can anyone suggest where I might be going wrong in modeling
the problem? My priors were non-informative but I have the same difficulty if I
use priors that contain estimates of the expected fatigue performance. The code
is presented below.
# Fatigue Test Results 12/02/03
# logS is natural log of stress range
# logNC is natural log of number of stress cycles to failure
or termination of test
# The test data are analyzed by linear regression with the
slope (m) forced to -3
model;
{
for( i
in 1 : N ) {
logNC[i] ~
dnorm(mu[i],tau)I(lower[i],)
}
for( i
in 1 : N ) {
mu[i] <- logA + m * logS[i]
}
tau ~
dgamma(0.001,0.001)
logA ~
dnorm( 0.0,1.0E-6)
sd <-
1 / pow(tau, 0.5)
des
<- logA-2*sd
}
# Data - there are 3 tests to failure and 6 censored results
list(m=-3, N=9)
logS[] logNC[] lower[]
4.162003211 NA 16.323482481
4.207673248 NA 16.323482481
4.141546164 16.323482481 0.000000000
4.633757643 14.539309148 0.000000000
4.620058798 NA 14.539309148
4.544358047 NA 14.539309148
4.996536370 NA 13.416783697
5.107156861 13.416783697 0.000000000
4.962844630 NA 13.416783697
END
# initializations for 3 chains
list(tau=0.01)
list(tau=1)
list(tau=100)
# Results
node
mean sd MC
error 2.5% median 97.5% start sample
des 28.07 0.9472 0.00673 26.64 28.23 28.56 20001 300000
logA 28.98 0.7283 0.005492 28.61 28.88 29.97 20001 300000
logNC[1] 16.78 1.164 0.007893 16.33 16.57 18.34 20001 300000
logNC[2] 16.72 1.099 0.007732 16.33 16.52 18.25 20001 300000
logNC[5] 15.24 1.154 0.007971 14.59 15.06 16.9 20001 300000
logNC[6] 15.42 1.205 0.008457 14.67 15.26 17.09 20001 300000
logNC[7] 14.11 1.134 0.00786 13.47 13.93 15.75 20001 300000
logNC[9] 14.19 1.192 0.008069 13.49 14.02 15.84 20001 300000
sd 0.4589 0.7413 0.006064 0.1462 0.326 1.519 20001 300000
tau 13.1 12.57 0.06402 0.4334 9.41 46.77 20001 300000