The following data came from an accelerated life test conducted on insulating fluid. The accelerating stress is voltage.
First, we check what should be the base survival function
As a result of these plots, we choose the log Normal base distribution over the Weibull and decide to exclude 32 KV in a preliminary analysis.
Now the lines are more parallel.
From here we see that - assuming a common sigma at all voltage levels - log voltage has linear (non-constant) effect on the location parameter of log failure time.
Now we exclude all voltage levels but 38 KV:
Now we exclude everything but voltage 36 KV.
Now we exclude everything but voltage 34 KV.
Now we exclude everything but voltage 30 KV.
Now we exclude everything but voltage 28 KV.
Now we exclude everything but voltage 26 KV.
If we add the log-likelihood for the last six JMP outputs we get the value -88.8027. This value corresponds to the log-likelihood for the model that assumes separate log-normals at all the voltage levels 26, 28, 30, 34, 36, and 38. This model has 12 parameters.
Now consider the model that assumes a common sigma at all voltage levels and a linear relationship of the location parameter of log failure time with log voltage. As we saw above for this model the loglikelihood is -95.0510. This model has 3 parameters.
So the difference in log likelihood multiplied by two for the two models is 2*[-88.8027-(-95.0510)]=12.4966
The .05 critical value for Chi-Square distribution with 9 d.f. is 16.92 so there is no compelling reason to reject the model that assumes a common sigma at all voltage levels and a liner relationship of the location parameter of log failure time with log voltage. Remember, however, that we excluded the 32 KV voltage level in this whole analysis
