There exist two different types of mathematical models that are widely used in reliability analysis: Binary-State System (BSS) and Multi-State System (MSS). Almost every system consists of more than one component. The importance of individual components for the system can be quantified by Importance Measures (IM). One of the most commonly used IM is the Birnbaum Importance (BI). The BI has been defined for the BSS. Development of this measure for the MSS is considered in this paper. New methodological approach based on the use of the Logical Differential calculus is used. The application of this approach allows definition of new equations for computation of the BI for system with series and parallel structure. Keywords: reliability, importance measure, birnbaum importance, multi-state system, logical differential calculus.
