Minimum upset/failure threshold statistics of devices for HERO/EMV testing

Statistical models for minimum current thresholds of electro-explosive devices (EEDs) have historically employed Gaussian (or Normal) distribution functions when extrapolating to low-level firing probabilities. However, the Gaussian distribution is rather poor for making extrapolations to extrema and, at very low probabilities, often becomes negative which is clearly unphysical. The purpose of this paper is to further investigate the distribution function of EED thresholds through experimentally measuring the threshold of micro-fuses (acting as EED bridgewire surrogates). The Generalized Log-Logistic distribution was determined to have the best fit for the full set of empirical data. However, it was determined that the extreme values (i.e. minimum device thresholds) could be better modeled through application of the Generalized Pareto Theorem. Distribution parameters and associated confidence intervals are statistically determined through maximum likelihood estimation (MLE) methods.