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A distinct characteristic of multistate systems (MSS) is that the systems and/or their components may exhibit multiple performance levels (or states) varying from perfect operation to complete failure. MSS can model behaviors such as shared loads, performance degradation, imperfect fault coverage, standby redundancy, limited repair resources, and limited link capacities. The nonbinary state property of MSS and their components as well as dependencies existing among different states of the same component make the analysis of MSS difficult. This paper proposes efficient algorithms for analyzing MSS using multivalued decision diagrams (MDD). Various reliability, availability, and performability measures based on state probabilities or failure frequencies are considered. The application and advantages of the proposed algorithms are demonstrated through two examples. Furthermore, experimental results on a set of benchmark examples are presented to illustrate the advantages of the proposed MDD-based method for the performability analysis of MSS, as compared to the existing methods.