On the extension of Importance Measures to complex components

Importance Measures are indicators of the risk significance of the components of a system. They are widely used in various applications of Probabilistic Safety Analyses, off-line and on-line, in decision making for preventive and corrective purposes, as well as to rank components according to their contribution to the global risk. They are primarily defined for the case the support model is a coherent fault tree and failures of components are described by basic events of this fault tree. In this article, we study their extension to complex components, i.e. components whose failures are modeled by a gate rather than just a basic event. Although quite natural, such an extension has not received much attention in the literature. We show that it raises a number of problems. The Birnbaum Importance Measure and the notion of Critical States concentrate these difficulties. We present alternative solutions for the extension of these notions. We discuss their respective advantages and drawbacks. This article gives a new point of view on the mathematical foundations of Importance Measures and helps us to clarify their physical meaning. - Highlights: • We propose an extension of Importance Measures to complex components. • We define our extension in term minterms, i.e. states of the system. • We discuss the physical interpretation of Importance Measures in light of this interpretation