Component assignment of circular k-out-of-n: G balanced system with 2 sectors considering component degradation

Balanced systems are widely used in the aerospace and military services featuring the symmetry structure with spatially distributed components, which increasingly becomes an important issue in the research field of the reliability theory. This paper studies a circular k-out-of-n: G balanced system with 2 sectors, which is operating if at least k components in each sector are working. In terms of the definition of a circular k-out-of-n: G balanced system with 2 sectors, we consider that if a component fails in one sector, the other unit of the same pair is forced down immediately to remain the symmetry of this sector. In addition, there is the same number of components in another sector has to be shut down in order to keep balance among all sectors. First, based on the proposed system balance condition, the system reliability model is presented based on minimal path sets. Second, considering the gamma degradation process of components, the optimization model is established to find the optimal component assignment scheme and the assignment time for maximizing the lower boundary of the system reliability during the required mission time. Third, the delta-importance (DI) based heuristics are developed to solve the model. The analytical results and the numerical experiment illustrate the efficiency of models and the solving method, shedding light on making design and maintenance strategy of balanced systems.