Sequential designs for efficient estimations of voltage percentiles in breakdown experiments

Dielectric breakdown (BD) is a common issue in high-voltage (HV) equipment. Since BD is a stochastic phenomenon, dielectric performance is typically characterised using the voltage where BD occurs with 50% probability,U50. However, determining voltages at which BD is increasingly unlikely is of greater technical relevance; for example, from the perspective of standardised certification tests for switchgear, the 2% BD probability voltage,U02, is of particular interest. Unfortunately, a statistically robust estimation of such low quantiles requires comparatively long test series, and a general analogue of the “up-down” method for efficiently estimatingU50in BD experiments has not been established in the HV industry. We therefore investigate two sequential designs for estimating quantiles of the BD response curve: an optimal Bayesian design and a non-parametric scheme based on the Robbins-Monro algorithm. We compare their efficiencies in terms of the number of voltage applications required to estimateU02with a given accuracy, first using synthetic data and subsequently by conducting BD experiments on an air-insulated sphere-plane electrode configuration. Both designs outperform uniform random voltages. More importantly, their comparison highlights the benefits of non-parametric approaches for response curves of unknown functional form.