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