On the assessment of extremely low breakdown probabilities by an inverse sampling procedure

When assessing extremely low breakdown probabilities for selfrestoring gaseous insulation by automatic equipment, it is often more important to keep the actual number of breakdowns low, rather than to control the total number of voltage applications. In order to achieve this, one might use an inverse sampling procedure that commences the voltage application at a very low level, followed by applications at stepwise increased levels until a breakdown occurs. Following a breakdown, the procedure is restarted at the initial level. The procedure is repeated until a predetermined number of breakdowns have occurred, and the average and standard deviation of the observed first breakdown levels are recorded. In this paper we investigate the statistical properties of such a procedure when the underlying flashover probability function is a double exponential distribution. We describe the relation between the mean of the first breakdown level and the single-shot flashover probability at this mean level, and we show how the sample mean and standard deviation of the first breakdown level may be used to assess this relation in an actual experiment. Finally, we indicate that the results for the double exponential flashover probability function may serve as a good approximation, also when other flashover probability functions are assumed.