In this paper, some well-known consecutive \(\varvec{k}\) -type systems, including linear consecutive- \(\varvec{k}\) -out-of- \(\varvec{n}\) : F systems and linear \(\varvec{l}\) -consecutive- \(\varvec{k}\) -out-of- \(\varvec{n}\) : F systems without/with overlapping, are generalized by using more general failure patterns. Finite Markov chain imbedding approach (FMCIA) is applied in a new way for evaluating reliabilities of these generalized new systems. Some illustrative examples are provided for demonstrating the theoretical results established here and also for showing the efficiency of the computational process. Finally, some possible applications and generalizations are mentioned.
