Application of Multiple-Valued Logic in Importance Analysis of k-out-of-n Multi-state Systems

Multi-State Systems (MSSs) represent one of the basic approaches used in reliability analysis. They define several performance levels at which the system and its components can operate. A special type of a MSS is k-out-of-n system whose instances can be found in complex systems with redundant components, such as distribution networks. In this paper we deal with importance analysis of such systems using direct partial logic derivatives. We present how these derivatives can be used to compute structural and Birnbaum's importance of system components, and we derive an algorithm for efficient calculation of Birnbaum's importance using multi-valued decision diagrams.