A Bayesian Estimation of Confidence Limits for Multi-state System Vulnerability Assessment With IEMI

Abstract

A Bayesian approach based on the vulnerability distribution is proposed to estimate the confidence limits of the state probability and the threat level of multistate electronic systems interfered by intentional electromagnetic interference (IEMI). The vulnerability distribution is used to describe the state probability function of the multi-state system (MSS) for a given IEMI threat level. When a small number of test samples are under a specific threat level and prior MSS information is known, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">posterior</i> estimation of the state probability function can be obtained based on Bayesian theory. Furthermore, to effectively apply the state probability function to assess the vulnerability of the MSS, the uncertainty of the state probability function is discussed. Considering state probabilities under the same threat level as random variables, all these state probabilities also follow the Dirichlet distribution. Thus, the confidence limits of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">posteriori</i> state probability and the threat level can be inferred by the marginal distribution of the state probability, which is induced by combining the Dirichlet and vulnerability distributions. Finally, a case study is given to demonstrate the details of the calculation process of the vulnerability distribution, the state probability function, and the confidence limits under a lognormal distribution.