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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 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.
