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An application of physics-based statistics in electrical engineering

The most widely accepted and used definition of probability is the relative-frequency definition. Strict adherence to this interpretation of probability requires the empirical development of statistical models from measured data. Using this definition of probability usually results in statistical models that are adequate for predicting the occurrence of the most common events, i.e., events near the mean. However, experience has shown that the resulting statistical models are often not adequate for predicting the occurrence of rare or extreme events, for which little or no data exist. In electrical engineering and the other physical sciences, an alternative approach exists for developing the statistical models. This approach is predicated on the existence of valid deterministic models of the phenomena or interaction of interest. The statistical models are derived from the deterministic models by making assumptions about the behavior of the parameters in the deterministic models. Physics-based statistical modeling can be applied to derive both strength and stress distributions. In the present paper, a strength example is developed-the thermal failure of semiconductor devices subjected to electrical overstress. Typical comparisons of predicted failure, based on the derived distributions, to measured data are presented.