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Article On the Notion of Discrete-Time Signature and Some Associated Properties and Results(Cambridge University Press, 2026) Balakrishnan, Narayanaswamy; Yi, He; Goroncy, AgnieszkaIn this work, by considering coherent systems comprising independent components with discrete lifetimes, we introduce the notion of discrete-time signature and then discuss some of its properties. With the use of the introduced signature, a stochastic ordering result is also established. We then introduce transformation formulas for the discrete-time signature to facilitate the comparison of systems of different sizes. Some examples are also presented to illustrate all the results developed here.Article A General Type of Linear Consecutive-K Systems(Springer, 2026) Yi, He; Balakrishnan, Narayanaswamy; Li, XiangIn this paper, some well-known consecutive k-type systems, including linear consecutive-k-out-of-n: F systems and linear l-consecutive-k-out-of-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.
