Methods for statistical analysis of the breakdown voltage of vacuum gaps

Dielectric testing of equipment is performed for different duties including the lightning impulse voltage (LIV). In cases where vacuum interrupters (VI) are used, the determination of the critical LIV value poses challenges due to the statistical nature of the breakdown in vacuum [1, 2]. Consequently, it is required to evaluate the dielectric behavior of a large number of specimens in order to obtain statistically significant values for the breakdown voltage. Especially during early development testing and for quality control procedures that provide statistical significance even with smaller test batches are highly desirable. The idea behind the methods presented here is, that tests that yield a numerical value for the breakdown voltage provide greater information as compared to those that are based on a pass/fail criterion [1, 2]. In this paper, the always breakdown method was used in dielectric testing to create a set of numerical values for a number of VIs. Experimental data were reviewed and converted into a function relating breakdown probability to the applied LIV voltage.Furthermore, the statistical significance required for smaller test batches is established by assuming that a certain critical level needs to be fulfilled with a high probability. In the case of dielectric characterization, this means whether a breakdown value $\mathrm{U}_{\mathrm{d}}$ is above or below a critical value $\mathrm{U}_{\mathrm{c}}$ (limit voltage). The goal is to determine the probability of a larger number of pieces (e.g. a batch) having a breakdown voltage greater than the critical value. This method produces two probabilities as a result and defines a range or two trendlines in which a derived ratio R can be compared by means of sequential testing. Here R respectively log(R) describes the ratio of the likelihoods of a positive or negative assignment. With the help of the position of R with respect to the trendline, the desired statistical significance can be achieved.