A Generalized Multiple-Valued Decision Diagram for Reliability Analysis of Fault-Tolerant Systems

Binary Decision Diagrams (BDDs) and their extensions multiple-valued decision diagrams (MDDs) have been adapted for reliability analysis of fault tolerant systems. Particularly, the MDDs are used to solve traditional coverage models (CMs) where an uncovered component failure may lead to system failure without constraint. This paper presents a new family of decision diagrams, generalized multiple-valued decision diagrams (GMDDs) for the latest irrelevancy coverage model (ICM). In contrast to traditional CMs, the ICM can detect and isolate components whenever they become irrelevant due to the failures of other components, and thus an uncovered component failure can only lead to system failure with the constraint when the component is relevant. Compared with the traditional MDD approach, the GMDD can handle constrained uncovered component failures, and it can incorporate general imperfect fault coverage modelling, including the ICM and traditional CMs.