2 results
Search Results
Now showing 1 - 2 of 2
Article Linear Two-Dimensional Consecutive K-Type Systems in Multi-State Case(Elsevier Sci Ltd, 2026) Yi, He; Balakrishnan, Narayanaswamy; Li, XiangIn the context of consecutive k-type systems, multi-state system models are only considered in the onedimensional 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 1-connected-(k, r)-out-of-(m, n): G systems without/with overlapping, and multi-state linear 1-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.Article Multi-State Linear Three-Dimensional Consecutive k-Type Systems(Cambridge Univ Press, 2026) Yi, He; Balakrishnan, Narayanaswamy; Li, XiangConsecutive $k$-type systems have become important in both reliability theory and applications; in spite of a large literature existing on them, three-dimensional consecutive $k$-type systems have not yet been studied for multi-state case. In this paper, we introduce several different types of multi-state linear three-dimensional consecutive $k$-type systems for the first time, with due consideration to possible overlapping of failure blocks. The finite Markov chain imbedding approach is then used for the derivation of their reliability functions with state spaces and transition matrices provided in a novel way, and the involved computational process is illustrated through several numerical examples. Finally, some possible applications of the work and potential extensions are pointed out.
