Yi, H.Balakrishnan, N.Li, X.2026-02-052026-02-0520260951-832010.1016/j.ress.2026.1122152-s2.0-105027639135https://doi.org/10.1016/j.ress.2026.112215https://hdl.handle.net/20.500.14411/11141In the context of consecutive k -type systems, multi-state system models are only considered in the one-dimensional case and not in the two-dimensional case due to the complexity involved. In this paper, we consider several linear two-dimensional consecutive k -type systems in the multi-state case for the first time, as generalization of consecutive k -out-of- n systems and l -consecutive- k -out-of- n systems without/with overlapping. These systems include multi-state linear connected-(k , r)-out-of-(m, n): G systems, multi-state linear connected-(k , r)-or-(r , k)-out-of-(m, n): G systems, multi-state linear l -connected-(k , r)-out-of-(m, n): G systems without/with overlapping, and multi-state linear l -connected-(k , r)-or-(r , k)-out-of-(m, n): G systems without/with overlapping. We then derive their reliability functions by using the finite Markov chain imbedding approach (FMCIA) in a new way. We also present several examples to illustrate all the results developed here. © 2026 Elsevier Ltd.eninfo:eu-repo/semantics/closedAccessConsecutive K-Type SystemFinite Markov Chain Imbedding Approach (FMCIA)Multi-State SystemSystem Without/With Overlapping ComponentsTwo-Dimensional SystemArticle