Reliability analysis of consecutive-k-out-of-r-from-n subsystems: F balanced systems with load sharing

In this paper, a consecutive-k-out-of-r-from-n subsystems: F balanced system with load sharing is proposed, which takes both linear and circular structures into consideration. Such a system has n subsystems and each subsystem consists of several sectors that have multiple components. Each subsystem should keep balance when it works and the concept of balance means that the number of working components should be the same in any sector belonging to the same subsystem. The system maintains balance by forcing down working components to standby or resuming standby components to operate. The failure or standby of a component will result in a higher load on each remaining working component, thereby inducing a higher hazard rate for them. The whole system fails if it contains a set of r consecutive subsystems in which at least k subsystems break down. The Markov process method and finite Markov chain imbedding approach are applied to analyze the system reliability. Numerical examples are presented to show the effectiveness of the studied model and proposed method.