Heterogeneous redundancy optimization for multi-state series–parallel systems subject to common cause failures

Components will fail when loads (such as humidity, temperature, vibration, shock) are beyond the limits, which is a kind of common cause failures. In order to provide a desired level of reliability with minimum cost, the optimal model of multi-state series–parallel system subject to this kind of common cause failures is formulated. The universal generating function is adapted to analyze the reliability of multi-state system with mixing of components of different types, and genetic algorithm is used to solve the optimal model. A numerical example is illustrated to demonstrate the proposed method. The results show that common cause failures make the redundancy allocation strategy different. To provide the desired level of reliability with minimum cost, the mixture of components of different types is a very effective method.