MDD-based performability analysis of multi-state linear consecutive-k-out-of-n: F systems

A multi-state linear consecutive-k-out-of-n: F system, MLC(k,n) consists of n components ordered in a line, which fails if at least k consecutive components have failed. It abounds in real-world applications such as wireless sensor networks, microwave station networks, and oil pipeline systems. Performability of an MLC(k,n) system is concerned with probability that the system performs at a performance state characterized in terms of the largest number of consecutive failed components. This paper proposes a multi-valued decision diagram (MDD)-based approach to model and evaluate performability of an MLC(k,n) system with heterogeneous components following arbitrary lifetime distributions. The proposed approach encompasses a novel and efficient MDD model generation procedure. Both complexity analysis and illustrative examples are provided to show efficiency of the proposed MDD approach. As demonstrated through examples, the proposed MDD approach is also applicable to MLC(k,n) systems with non-identical reparable components and component importance analysis.