Redundancy allocation optimization for multi-state system with hierarchical performance requirements

Conventional redundancy allocation optimization model is usually measured by single performance. It meets difficulties in modeling the redundancy allocation optimization of multi-state system (MSS) with hierarchical performance requirements. This study proposes a generalized optimization model for MSS. This model concentrates on the redundancy allocation problem of the MSS with the inter-level dependent performances requirements. In the case of the minimum cost or maximum availability of the system, the aim of this model is to optimize system configuration, such as the economic numbers and versions for the multilevel heterogeneous components with known reliability and cost characteristics. Firstly, two algorithms to evaluate the system availability are introduced. A modified universal generation function (UGF) algorithm combining hierarchical operators is developed to evaluate the accurate availability for the system. Then the recursive algorithm (RA) is also used to obtain the lower and upper bounds of system availability. Secondly, compared with the traditional optimization model for the single level system, the proposed model for the hierarchical system has more decision variables which lead to difficult computation. Therefore, the genetic algorithm (GA) is applied to solve the redundancy allocation, especially the optimal numbers and versions of the different-level components simultaneously. Finally, a realistic power system verifies the correctness and validity of the suggested model. In conclusion, the results show that the above model tends to be more flexible and effective in the redundancy allocation optimization. Furthermore, this model helps the engineer in the reliability design optimization for the complex systems.