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Article Generalized Chi-Squared Based Goodness-of-Fit Tests under Progressive Type-II Censoring for Exponential and Weibull Distributions(Taylor & Francis Inc, 2026) Schmiedt, Anja B.; Balakrishnan, Narayanaswamy; Cramer, ErhardWe propose new goodness-of-fit tests for exponentiality based on progressively Type-II censored data. These tests utilize scale-invariant statistics obtained from the Mahalanobis norm of normalized order statistics, leading to three test statistics, corresponding to L-2(-), L-1(-), and L-infinity-norms of centered uniform spacings. Exact and asymptotic distributions of these statistics are presented. A power study evaluates the proposed tests against existing benchmarks across various alternative distributions and censoring plans, demonstrating superior performance in cases with small and moderate sample sizes. Furthermore, we extend the methodology to approximate goodness-of-fit tests for Weibull distributions via power transformation, ensuring robustness w.r.t. the approximated significance level under unknown shape parameters. An illustrative data example confirms the practical applicability of our tests. Our findings highlight the potential for further extending goodness-of-fit tests under progressive Type-II censoring to other null distributions.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.Article Acceptance Sampling Plan under Step Stress Accelerated Life Test for One-Shot Devices(Elsevier Sci Ltd, 2026) Lin, Chien-Tai; Balakrishnan, Narayanaswamy; Ling, Man-HoAcceptance sampling plans are essential in many manufacturing industries, serving as a statistical method to decide whether to accept or reject a batch of products based on the quality of a sample. The demand for reliable assessment methodologies has grown increasingly important as devices become more reliable under normal operating conditions. This trend poses challenges for reliability assessments, especially when there is limited failure data from tests. To address this, accelerated life testing (ALT) is widely employed to induce rapid failures for reliability analysis. This paper presents a comprehensive study of acceptance sampling plans under step-stress ALT (SSALT) for one-shot devices. We propose a tailored acceptance sampling plan that incorporates SSALT principles to enhance decision-making regarding product acceptance. Our methodology enables the determination of acceptable quality thresholds while evaluating the associated producer's and consumer's risks. Moreover, it can determine the minimum sample size required to ensure that both risks are adequately addressed, as well as to identify the optimal percentage of test items to examine at various testing stages. Two illustrative examples are provided to demonstrate the developed optimal acceptance sampling plans. This research highlights the significant impact of the choice of reliability index and stress pattern on inspection allocation.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 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 On Optimal Allocation of Redundancies in Random Weighted Coherent Systems(Wiley, 2026) Sahoo, Tanmay; Hazra, Nil Kamal; Balakrishnan, NarayanaswamyUnlike the ordinary coherent systems, a random weighted coherent system captures components' disparity. Its performance is measured by some appropriate measure of contributions made by all of its components. In this paper, we consider random weighted coherent systems, defined based on the survival capacity, with three different survival mechanisms, namely, Types-I, II, and III. Then, we study the optimal active redundancy allocation policy as well as the optimal assembly method of random weights in a random weighted coherent system. We provide several numerical examples to illustrate all the results established here.
