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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