Mixed Weibull distribution model of DC dielectric breakdowns with dual defect modes

Abstract

This work provides physical insight into common statistical models for DC dielectric breakdown field strengths. Voltage step-up tests were performed on low density polyethylene films. The merits of generalizations to widely-used empirical Weibull models are discussed. The cumulative probability distributions of the breakdown fields were fit to standard two-and three-parameter Weibull distributions. Mixed two-parameter Weibull distributions, sometimes used in the literature to model multiple breakdown modes, were found to yield the best fits to the data. In addition, the same data were fit to a physically-motivated dual-defect mean field model incorporating both low-and highenergy defect modes with different defect densities; this produced a much better fit than single-defect mean field models. Values obtained for the mean defect energies and densities were within the ranges expected from independent determinations of these intrinsic materials properties. By incorporating these physicsbased concepts into traditionally empirical models, their accuracy and utility can be extended. The mixed Weibull distribution and the dual-defect model predicted very similar cumulative distributions of LDPE breakdown data, suggesting that mixed Weibull distributions may reflect similar multiple defect modes used in dual-defect models. Theories of DC breakdown, based on distributions of microscopic defects in disordered insulating materials may provide improved guidance in understanding the physical origins of empirical parameters used in statistical methods to characterize breakdown properties.

Perspectives on the Distributions of ESD Breakdowns for Spacecraft Charging Applications

“… Breakdown is not well characterized by as single number. Consider a probability distribution that depends not only on the material, but the conditions it is subjected to over time [13,17]. The acceptable probability need to be determined by considering mission objectives and tolerances.…”

“… Physics-based or even well-chosen empirical models can estimate behaviour of materials for times and conditions not achievable with testing [13,17].…”

“…For example, static voltage endurance time (SVET) experiments hold a sample below its nominal breakdown voltage and measure the time to breakdown. Results can be fit to empirical or physical models in order to extrapolate the results to the comparatively very slow ramp rates and much longer times typical of spacecraft missions [13,17].…”

Pre-breakdown arcing as proxy for DC dielectric breakdown testing of polymeric insulators

“…Although the analysis presented above is entirely empirical, we offer here a plausible physical context [2,4,17]. Consider low-energy physical defects such as bond bending.…”

Nonlinear Least Squares Estimation for Parameters of Mixed Weibull Distributions by Using Particle Swarm Optimization

“…The results indicate that the mixed Weibull distribution model has a higher accuracy compared with other methods. Andersen and Dennison [6] developed a mixed Weibull Distribution Model of DC Dielectric Breakdown failures, as these failures incorporate both low-and high-energy defect modes. Ghavijorbozeh and Hamadani [7] applied the mixed Weibull distribution in the machine reliability analysis for the Cellular manufacturing system.…”