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Article Circular One/Two/Three-Dimensional Consecutive k-Type Systems(Springer, 2026) Yi, He; Balakrishnan, Narayanaswamy; Li, XiangIn this paper, several circular one/two/three-dimensional consecutive k-type systems are studied, including circular consecutive-k-out-of-n: F systems, circular l-consecutivek-out-of-n: F systems without/with overlapping, circular connected-(k(1), k(2))-outof-(n(1), n(2)): F systems, circular l-connected-(k(1), k(2))-out-of-(n(1), n(2)): F systems without/ with overlapping, circular connected-(k(1), k(2), k(3))-out-of-(n(1), n(2), n(3)): F systems, and circular l-connected-(k(1), k(2), k(3))-out-of-(n(1), n(2), n(3)): F systems without/with overlapping. Reliability functions of these systems are studied using finite Markov chain imbedding approach (FMCIA). Some illustrative examples are provided, and possible applications and generalizations of the established results are also mentioned.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.Article Nonparametric Tests for Comparing Reliabilities of Coherent Systems at Specific Mission Time(IEEE-Inst Electrical Electronics Engineers Inc, 2026) Xu, Xuan; Zhu, Xiaojun; Balakrishnan, Narayanaswamy; Ng, Hon Keung TonyReliability analysis of coherent systems is critical for evaluating the performance of systems whose functionality depends on the reliability of their components. Traditional parametric methods for comparing reliabilities of coherent systems assume a specific probability distribution for component lifetimes, which may result in inaccurate results when these model assumptions are violated. This article introduces nonparametric procedures using system-level data with known signatures to compare the reliabilities of systems. The proposed methodology avoids parametric distributional assumptions for component lifetimes while relying on the standard assumption in signature-based reliability analysis. Specifically, a two-sample likelihood ratio test procedure is proposed to demonstrate a component or system with superior reliability. Monte Carlo simulations are performed to evaluate the performance of the proposed methods. Furthermore, we examine the effect of system structure on test power and determine favourable structures to enhance the power performance of the test. Practical examples are used to illustrate the proposed test procedures.
