Efficient analysis of multi-state k-out-of-n systems

Abstract

Many practical systems are multi-state k-out-of-n systems with independent, non-identical components, where the system and its components have multiple performance levels and maybe multiple failure modes. Furthermore the system may have different requirements on the number of working components (i.e., value of k) for different system state levels. This paper proposes a new analytical method based on multi-valued decision diagrams (MDDs) for the reliability analysis of such multi-state k-out-of-n systems. MDDs have recently been applied to the reliability analysis of general multi-state systems (MSS). In this work, we make the new contribution by proposing a novel and efficient algorithm for constructing the system MDD that is designed to fully make use of the well-defined k-out-of-n structure. Examples show how the MDD models are generated using the proposed algorithm, and are then evaluated to obtain the system reliability measures. Performance of the MDD-based method is compared with that of an existing recursive algorithm through a comprehensive benchmark study. Empirical results show that the proposed MDD-based method can offer lower computational complexity than the recursive algorithms, and it can be effectively applied to large practical cases for multi-state k-out-of-n systems.