Estimating the Probability Density Function of the Electromagnetic Susceptibility from a Small Sample of Equipment

International audienceThe failure risk of electronic equipment submitted to an electromagnetic aggression may be seen as the conditional probability that the susceptibility level of equipment is reached, knowing that a given constraint is applied. This paper focuses on the estimation of the probability density function of the susceptibility level of equipment. Indeed, the production variability of electric/electronic equipment under analysis implies that its susceptibility level may be considered as a random variable. Estimation of its distribution through susceptibility measurements of a limited set of available equipment is required. Either a Bayesian Inference (BI) or a Maximum Likelihood Inference (MLI) may be used for assessing the most probable density function. Above all, we highlight that they have to be used to delimit a set of probable distribution functions rather than the most probable one. It then provides realistic bounds of the failure probability at a given test level. First both types of inference are carried out on theoretical distributions. Then we compare the two methods on a virtual piece of equipment whose distribution is not known a priori but can be estimated a posteriori. Finally, we apply these inferences on a set of actual susceptibility measurements performed on several copies of equipment. We check that for extremely small sample size (a dozen) the Bayesian approach performs slightly better. However, above around 40, the two methods perform similarly. In all cases, the likelihood estimations provide a clear statement of the probabilistic estimation of the statistics of susceptibility level given a limited sample of pieces of equipment