Estimation for the Weibull Power Law Parameters in the Step-up Voltage Test

In assessing the insulation withstand level of the electric apparatus, the step-up test method is used. However, we have still many unknown matters regarding the treatment of the results. In this paper, we assume that the underlying probability distribution of failure time with a constant 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 estimate 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 likelihood 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 compare 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 deviation. 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.