Importance Measures of Multi-State Components in Multi-State Systems

Abstract

In system engineering a practical and difficult problem is the identification of those components that mostly influence the system behaviour with respect to safety and reliability. In this regard, the information provided by importance measures gives useful insights for the safe and efficient operation of the system. Importance measures have received attention since the early times of risk and reliability analysis and have been defined in several ways for binary components in binary systems. Yet, there are applications for which a multi-state modelling of components and systems is required. This is the case of manufacturing production lines and power generation systems in which the components and the overall systems can operate at different, discrete, levels of performance so that the output provided is a fraction of the nominal design capacity. A similar situation occurs in transportation systems. In the limit, there is the case of systems whose performances are characterized in terms of an infinite set of continuous states. These are, for example, the passive safety systems whose utilization is becoming more and more significant in the advanced and innovative concepts of nuclear reactor design. In this paper, the definitions of the most frequently used classical importance measures are generalized to multi-state systems constituted by multi-state components. The extensions introduced characterize the importance of a component achieving a given level of performance with respect to the overall multi-state system unavailability and performance. The informative content provided by the introduced measures is illustrated on a simple multi-state system.