On the assessment of extremely low breakdown probabilities by an inverse sampling procedure [gaseous insulation]

First breakdown voltages obtained under the inverse sampling procedure assuming a double exponential flashover probability function are discussed. An inverse sampling procedure 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. The authors derive the relation between the flashover probability function and the corresponding distribution of first breakdown voltages under the inverse sampling procedure, and show how this relation may be utilized to assess the single-shot flashover probability corresponding to the observed average first breakdown voltage. Since the procedure is based on voltage applications in the neighbourhood of the quantile under investigation, the procedure is found to be insensitive to the underlying distributional assumptions