Joint reliability of linear consecutive k-type systems with shared components in a zigzag structure

In this paper, four different types of linear consecutive-k systems with shared components in a zigzag structure—linear consecutive-k-out-of-n: F systems, linear consecutive-k-out-of-n: F systems with sparse d, linear m-consecutive-k-out-of-n: F systems without overlapping, and linear m-consecutive-k-out-of-n: F systems with (at most) p overlapping—are considered. The joint reliability functions of these systems are obtained by using finite Markov chain imbedding approach (FMCIA) in a novel way, which provide more information about performance of the systems than individual reliability functions of them. Some numerical examples are presented to demonstrate the computational process of the developed method, and possible applications and generalizations are also briefly mentioned.