More accurate breakdown voltage estimation for the new step-up test method in the Gumbel distribution model

The estimation problems for the conventional step-up method (the observed breakdown voltages are not given at all) and the new step-up method (some of the observed breakdown voltages are given) are analyzed when the underlying probability distribution (of breakdown voltage level) is assumed to be Gumbel distributions for minima and maxima. The new step-up test method has advantages compared to the conventional method: (1) the confidence intervals of the estimates become smaller and (2) the estimates can be obtained with higher probability. In some case of real step-up breakdown voltage test, a fit of the Gumbel distribution to the data case is found to be superior to that of the normal distribution, which suggests the usefulness of the Gumbel distribution for the underlying distribution in the step-up breakdown voltage test.