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A Review of Reliability Assessment for Consecutive k-out-of-n Systems
Review Article  ·  Published: 20 April 2026
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ICCK Transactions on Systems Safety and Reliability
Volume 2, Issue 2, 2026: 112-122
Review Article Free to Read

A Review of Reliability Assessment for Consecutive k-out-of-n Systems

by
Hao Xie Hao Xie 1
Songling Liu Songling Liu 1
Jiaying Rao Jiaying Rao 1
Zhitao Wu Zhitao Wu 2 ORCID
Chaonan Wang Chaonan Wang 1 * ORCID
1 College of Cyber Security, Jinan University, Guangzhou 510632, China
2 CEPREI, Jinan University, Guangzhou 510632, China
* Corresponding Author: Chaonan Wang, [email protected]
Volume 2, Issue 2
Volume 2, Issue 2 2026
Received: 12 March 2026 Accepted: 01 April 2026 Published: 20 April 2026 CrossMark
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DOI: 10.62762/TSSR.2026.526355
ARK: ark:/57805/tssr.2026.526355

Article Information

Published in ICCK Transactions on Systems Safety and Reliability
Volume/Issue Volume 2, Issue 2, 2026
Pages 112-122

Abstract

As engineering systems grow in scale and complexity, the classical consecutive k-out-of-n model has evolved significantly to address the challenges of component dependence and dynamic maintenance. This paper presents a comprehensive survey of these advancements, categorized into model extensions and assessment methodologies. We synthesize key variants adapted for practical scenarios, including consecutive k-within-m-out-of-n systems, m-consecutive-k-out-of-n systems, (n, f, k) and ⟨n, f, k⟩ systems, sparse $d$ systems, and complex models accounting for component dependence and repair mechanisms. Regarding reliability assessment, this paper evaluates the transition from analytical methods to scalable computational approaches like System Signatures and Universal Generating Functions (UGF). Furthermore, we identify a critical shift towards data-driven methodologies, highlighting how Graph Neural Networks (GNNs) are transforming the analysis of large-scale, multi-state systems. The review concludes by outlining a strategic roadmap for future research, emphasizing the integration of deep learning to achieve real-time reliability assessment and intelligent fault management.

Graphical Abstract

A Review of Reliability Assessment for Consecutive k-out-of-n Systems

Keywords

consecutive k-out-of-n reliability assessment multi-state systems universal generating functions

Data Availability Statement

Not applicable.

Funding

This work was supported without any funding.

Conflicts of Interest

The authors declare no conflicts of interest.

AI Use Statement

The authors declare that generative artificial intelligence was used in a limited capacity during the preparation of this manuscript. Specifically, GPT-5 was employed for optimizing figure presentation and proofreading the formatting of references. No AI tools were used for generating scientific content, analysis, or interpretations presented in this work. The authors take full responsibility for the accuracy, integrity, and originality of all content in this manuscript.

Ethical Approval and Consent to Participate

Not applicable.

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Cite This Article

APA Style
Xie, H., Liu, S., Rao, J., Wu, Z., & Wang, C. (2026). A Review of Reliability Assessment for Consecutive k-out-of-n Systems. ICCK Transactions on Systems Safety and Reliability, 2(2), 112–122. https://doi.org/10.62762/TSSR.2026.526355
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TY  - JOUR
AU  - Xie, Hao
AU  - Liu, Songling
AU  - Rao, Jiaying
AU  - Wu, Zhitao
AU  - Wang, Chaonan
PY  - 2026
DA  - 2026/04/20
TI  - A Review of Reliability Assessment for Consecutive k-out-of-n Systems
JO  - ICCK Transactions on Systems Safety and Reliability
T2  - ICCK Transactions on Systems Safety and Reliability
JF  - ICCK Transactions on Systems Safety and Reliability
VL  - 2
IS  - 2
SP  - 112
EP  - 122
DO  - 10.62762/TSSR.2026.526355
UR  - https://www.icck.org/article/abs/TSSR.2026.526355
KW  - consecutive k-out-of-n
KW  - reliability assessment
KW  - multi-state systems
KW  - universal generating functions
AB  - As engineering systems grow in scale and complexity, the classical consecutive k-out-of-n model has evolved significantly to address the challenges of component dependence and dynamic maintenance. This paper presents a comprehensive survey of these advancements, categorized into model extensions and assessment methodologies. We synthesize key variants adapted for practical scenarios, including consecutive k-within-m-out-of-n systems, m-consecutive-k-out-of-n systems, (n, f, k) and ⟨n, f, k⟩ systems, sparse $d$ systems, and complex models accounting for component dependence and repair mechanisms. Regarding reliability assessment, this paper evaluates the transition from analytical methods to scalable computational approaches like System Signatures and Universal Generating Functions (UGF). Furthermore, we identify a critical shift towards data-driven methodologies, highlighting how Graph Neural Networks (GNNs) are transforming the analysis of large-scale, multi-state systems. The review concludes by outlining a strategic roadmap for future research, emphasizing the integration of deep learning to achieve real-time reliability assessment and intelligent fault management.
SN  - 3069-1087
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -
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@article{Xie2026A,
  author = {Hao Xie and Songling Liu and Jiaying Rao and Zhitao Wu and Chaonan Wang},
  title = {A Review of Reliability Assessment for Consecutive k-out-of-n Systems},
  journal = {ICCK Transactions on Systems Safety and Reliability},
  year = {2026},
  volume = {2},
  number = {2},
  pages = {112-122},
  doi = {10.62762/TSSR.2026.526355},
  url = {https://www.icck.org/article/abs/TSSR.2026.526355},
  abstract = {As engineering systems grow in scale and complexity, the classical consecutive k-out-of-n model has evolved significantly to address the challenges of component dependence and dynamic maintenance. This paper presents a comprehensive survey of these advancements, categorized into model extensions and assessment methodologies. We synthesize key variants adapted for practical scenarios, including consecutive k-within-m-out-of-n systems, m-consecutive-k-out-of-n systems, (n, f, k) and ⟨n, f, k⟩ systems, sparse \$d\$ systems, and complex models accounting for component dependence and repair mechanisms. Regarding reliability assessment, this paper evaluates the transition from analytical methods to scalable computational approaches like System Signatures and Universal Generating Functions (UGF). Furthermore, we identify a critical shift towards data-driven methodologies, highlighting how Graph Neural Networks (GNNs) are transforming the analysis of large-scale, multi-state systems. The review concludes by outlining a strategic roadmap for future research, emphasizing the integration of deep learning to achieve real-time reliability assessment and intelligent fault management.},
  keywords = {consecutive k-out-of-n, reliability assessment, multi-state systems, universal generating functions},
  issn = {3069-1087},
  publisher = {Institute of Central Computation and Knowledge}
}

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