Reliability analyses of linear two-dimensional consecutive k-type systems

In this paper, several linear two-dimensional consecutive k-type systems are studied, which include the linear connected-(k, r)-out-of- $(m,n)\colon\! F$ system and the linear l-connected-(k, r)-out-of- $(m,n)\colon\! F$ system without/with overlapping. Reliabilities of these systems are studied via the finite Markov chain imbedding approach (FMCIA) in a novel way. Some numerical examples are provided to illustrate the theoretical results established here and also to demonstrate the efficiency of the developed method. Finally, some possible applications and generalizations of the developed results are pointed out.