Multi-state balanced systems in a shock environment

Reliability analysis of balanced systems has become an important research topic. In previous studies, a balanced system only has two states, i.e., perfect functioning and complete failure. However, most practical systems have more than two states because of the complex system structure and complicated working environment. To fill in this research gap, a general multi-state balanced system is proposed by considering that the components in the system and the whole system both have multiple states. In this paper, component state transitions are assumed to be caused by external shocks. Based on the operating states of all components, the multiple states of the system are determined according to different system balance degrees, formulated by a balance function. Multi-state balanced systems based on state distance and symmetric state distance are constructed in detail based on two specific balance functions. The corresponding state probability functions and some other reliability indexes are derived by using a two-step finite Markov chain imbedding approach. Finally, numerical examples are presented and some future research topics are discussed.