An empirical approach for characterizing transistor emitter-base failure threshold probability density functions is presented. The data analyzed come from a program of experiments designed to test component failures due to electrical overstress transients. First, an empirical distribution is obtained which describes the variation of the relative width of a large set of measured failure threshold distributions. Using this distribution, a technique is presented for obtaining threshold distribution parameters when the mean failure threshold is assumed to be known, Second, a technique is presented for combining the distribution of relative width with a derived mean uncertainty estimate. This yields a probabilistic statement of the threshold distribution parameters based on the estimated mean and the described uncertainty distributions. This approach is used to provide probabilistic statements on threshold lower bounds. An example of the use of these techniques is included.