Threshold Level Crossings, Excursions, and Extrema in Immunity and Fading Testing Using Multistirred Reverberation Chambers

Theoretical statistics and probability distributions are presented for level-crossing characteristics and failure rates in mono- and multistirred reverberation chambers, with supporting experimental results. Measured frequency responses for the spectral moments of the stir data exhibit power-law dependencies regardless of the scalar or vector nature of the field. For d-dimensional homogeneous isotropic stirring involving d stir or scan actions, the length of excursions above a high threshold exhibits a Weibull distribution with shape parameter 2/d. For excursions below low thresholds, their size follows a transformed inverse first-kind confluent hypergeometric function distribution with the same shape parameter. Excursion lengths decrease inversely proportionally with the root mean square (rms) rate of fluctuation. A lower bound on the equivalent number of independent samples is obtained that depends on the rms rate of fluctuation and on the dimensionality of the stir domain. For uncertain test levels with Gaussian prior probability density function (PDF), the total PDF is obtained in closed form. Among several other results, an expression for the mean time between failures based on energy levels is obtained and validated experimentally.