Abstract
Decision diagrams, which are primarily based on Shannon’s decomposition theorem, can represent binary and multi-valued logical functions as graphs in the form that is both canonical and compact. Since 1993 when binary decision diagrams were first adapted and applied to the fault tree reliability analysis of binary-state systems, different forms of decision diagrams have been proposed for efficient reliability analysis of various types of complex systems in applications such as cloud computing, wireless sensor networks, social networks, Internet of Things, space exploration, etc. This chapter introduces basics of decision diagrams, and their recent advancements and state-of-the-art applications in the reliability analysis of multi-state systems and multi-phase systems.