An Efficient Multistate Multivalued Decision Diagram-Based Approach for Multistate System Sensitivity Analysis

Multistate systems (MSS) are systems in which the system and its components are characterized by multiple states or performance levels. Component importance or sensitivity analysis facilitates the identification of vulnerabilities within the system, and aids in the quantification of criticalities of the system components. Multistate component importance analysis poses unique challenges to existing methods that are primarily based on binary-state applications. This paper presents an analytical method based on multistate multivalued decision diagrams (MMDD) for multistate component importance analysis. The contribution of this work is two-fold: 1) a novel, efficient algorithm for directly generating an MMDD model from multistate capacity network specifications without inefficient enumeration of multistate minimal path or cut vectors; and 2) an efficient, exact MMDD-based approach for evaluating MSS reliability and importance measures. The advantages of the proposed method are illustrated through a comparison with existing methods, and through detailed analyses of three case studies.