Estimation of the Coverage Probability of S-Parameters for Safety-Critical Systems with Hotelling’s T2 Distribution

Safety-critical systems, such as medical products, industrial safety functions, or autonomous driving systems, rely not only on the knowledge of the actual system parameters, but it is imperative to also take statistic properties into account. Besides measurement uncertainties, sample variation can play an extraordinary role in the evaluation of the overall variation of a certain parameter. S-parameters are used to describe the linear behavior of high-frequency devices, such as cables. This paper focuses on the quantification of sample variation to satisfy predefined safety margins. First, statistic relations are deduced and presented. Afterwards, these results are verified by means of Monte Carlo simulations. It can be shown, that even for moderate sample sizes of about 50 observations, the Hotelling’s T2 distribution needs to be used to account for the uncertainty of the sample covariance matrix estimation. These general findings are adapted to S-parameter measurements and an application based on 9 cable measurements is presented.