A cost-integrated Birnbaum importance measure for multi-state systems with binary-state components

Importance analysis constitutes a fundamental tool in reliability engineering, extensively employed to identify critical components that exert significant influence on system reliability and to support decision-making in system optimization and resource allocation. The Birnbaum importance measure (BIM) is a representative method for a ssessing the extent to which variations in a component's reliability affect overall system reliability. For multi-state systems composed of binary-state components, this study incorporates the cost-reliability relationship into the conventional BIM framework and proposes a novel cost-integrated Birnbaum importance measure (CBIM). The CBIM accounts for both the reliability contribution of each component and its economic characteristics, thereby facilitating a more comprehensive evaluation of component significance. Theoretical relationships between CBIM and traditional BIM are explored, and the properties of CBIM are further analyzed. Numerical experiments demonstrate the effectiveness and practical applicability of CBIM in identifying critical components and enhancing system reliability.