In assessing the insulation withstand level of the electric
apparatus, the step-up test method is used. However, we have
still many un- known matters regarding the treatment of the re-
sults. In this paper, we assume that the underlying probability
distribution of failure time with a con- stant voltage level
follows a Weibull distribution and that an inverse power law
relationship between the mean lifetime and the imposed voltage
holds; that is, the Weibull power law is assumed. Under such
a condition, we first investigate whether we can es- timate the
unknown Weibull power law parameters using the breakdown voltage
results obtained from the step-up test. We assume two models:
one is the independence model, and the other is the cumulative
exposure model. When we use the maximum like- lihood estimation
(MLE) method, the estimation is well performed in both the models.
On the contrary, the method of least squares (LS), commonly used
for electric engineers in obtaining the Weibull parameters for
the breakdown voltage, performs badly. We com- pare the estimation
results between those using the MLE and those using the LS both
the models. The LS has a tendency to yield a bias for the Weibull
shape parameter, and it generates a larger standard devia- tion.
Consequently, the RMSE using the LS becomes larger than that
using the MLE. We conclude that the MLE is superior to the LS.
Regarding the model selection of which model between the independence
model and the cumulative exposure model should be used, we recommend
the cumulative exposure model from both viewpoints of the model
derivation and the RMSE.