Many real-world engineering systems such as aerospace systems, intelligent transportation systems and high-performance computing systems are designed to complete missions in multiple phases. These types of systems are known as phased-mission systems. Inspired by an industrial heating system, this research proposes a generalized linear sliding window system with phased missions. The proposed system consists of N nodes with M multi-state elements that are subject to degradation. The linear sliding window system fails if the cumulative performance of any r consecutive nodes is less than the pre-determined demand in any phase. The degradation process of each element is modeled by a continuous-time Markov chain. A novel reliability evaluation algorithm is proposed for the linear sliding window system with phased missions by extending the universal generating function technique. Furthermore, the optimal element allocation strategy is determined using the particle swarm optimization. The effectiveness of the proposed algorithm is confirmed by a set of numerical experiments.

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Existing research on multistate system reliability has mainly focused on one‐dimensional systems such as parallel systems, linear sliding window systems, and linearly consecutively connected systems. However, two‐dimensional networked systems widely exist in real‐world applications such as lighting systems, monitoring systems, and computer network systems. This research considers a two‐dimensional networked system consisting of multistate components. The system fails if the cumulative performance of any row or any column cannot meet a predetermined demand. A novel reliability evaluation algorithm is proposed for the considered two‐dimensional networked system by extending the universal generating function technique. Furthermore, the proposed model and reliability evaluation algorithm are extended to a two‐dimensional networked system with phased missions. The proposed models and algorithms are illustrated by a matrix heating system in a thermoforming machine.

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