Modifications to the von Laue statistical distribution of the times to breakdown at a polymer-oil interface

A statistical analysis has been undertaken to determine the statistical and formative times associated with breakdowns along a polymer-oil interface under impulse conditions. Early analysis was based on an assumption that the breakdown data followed the von Laue Distribution. However, it was found that in the Laue plots there were deviations from the expected straight line behavior at short times to breakdown, which may be due to a normal distribution in values of the formative times. In addition, the plots showed multiple straight line sections, which suggested that changes were occurring to the breakdown processes during the experimental run, or that more than one mechanism of breakdown was occurring. Values of the statistical time ts and the formative time tf were determined from the data by making choices on the straight line section to be considered, and ignoring the effects of the normal distribution on the derived values of ts and tf. The present paper is focused on further development of this statistical method, including a rigorous analysis of the experimental data, taking into account the effect that a normal distribution of the formative times has on the derived values of ts and tf. Optimal fits in terms of three parameters: ts, tf, and f (the standard deviation of the formative time) have been derived using Kolmogorov-Smirnov statistics to quantify the quality of fit. The quality of these fits and the applicability of this approach is discussed.