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On steady and time-dependent reliability measures of multi-state systems under maintenance by Lz-transform

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  • Bisht, Vaibhav
  • Bisht, Soni
  • Singh, S.B.

Abstract

This study analyzes a weighted K-out-of-n system using the Lz-Transform approach under a novel maintenance strategy, deriving dynamic reliability measures and proposing, for the first time, an algorithm for calculating steady-state availability. The strategy involves repairing failed components at an exponential rate α, transitioning them to the best-performing state, followed by degradation at rate β. A real-world case study of a warship's power system validates the approach, with dynamic reliability indices computed and compared to prior results, demonstrating the method's effectiveness. The analysis shows that reliability and availability depend on the system's minimum performance level (K). Initially, both metrics are perfect, but they decline over time. Systems with higher K values exhibit resilience, maintaining near-perfect reliability and availability under demanding conditions, while systems with lower K values experience significant declines. Availability remains slightly higher than reliability, reflecting the system's operational readiness. Additionally, the sensitivity of reliability to failure rates is examined, revealing how changes in failure rates impact system performance. The findings highlight the potential to enhance reliability and availability through the proposed maintenance strategy.

Suggested Citation

  • Bisht, Vaibhav & Bisht, Soni & Singh, S.B., 2025. "On steady and time-dependent reliability measures of multi-state systems under maintenance by Lz-transform," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).
    • Handle: RePEc:eee:reensy:v:264:y:2025:i:pb:s0951832025006167
    DOI: 10.1016/j.ress.2025.111416
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    References listed on IDEAS

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    1. Bo, Yimin & Bao, Minglei & Ding, Yi & Hu, Yishuang, 2024. "A DNN-based reliability evaluation method for multi-state series-parallel systems considering semi-Markov process," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    2. Anatoly Lisnianski, 2012. "L z -Transform for a Discrete-State Continuous-Time Markov Process and its Applications to Multi-State System Reliability," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel (ed.), Recent Advances in System Reliability, chapter 0, pages 79-95, Springer.
    3. Yan Li & Jiaqi Niu & Mengxue Xing & Jinzhi Chen, 2024. "Reliability modeling of weighted-k-out-of-n: G system under multiple failure modes with dependent components," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(13), pages 4880-4897, July.
    4. Jinlei Qin & Zheng Li, 2019. "Reliability and Sensitivity Analysis Method for a Multistate System with Common Cause Failure," Complexity, Hindawi, vol. 2019, pages 1-8, May.
    5. Vaibhav Bisht & S. B. Singh, 2024. "Interval valued reliability indices assessment of multi-state system using interval $$L_{z}$$ L z -transform," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(7), pages 3293-3305, July.
    6. Zhao, Xian & Han, He & Jiao, Chunhui & Qiu, Qingan, 2024. "Reliability modeling of k-out-of-n: F balanced systems with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    7. Chen, Guizhuang & Hu, Yuliang & Wang, Chaonan & Wu, Zhitao & Rong, Wenjing & Guan, Quanlong, 2025. "Efficient reliability analysis of generalized k-out-of-n phased-mission systems," Reliability Engineering and System Safety, Elsevier, vol. 253(C).
    8. Vaibhav Bisht & S. B. Singh, 2022. "Reliability Analysis of 8 × 8 SEN- Using UGF Method," Springer Series in Reliability Engineering, in: Mangey Ram & Hoang Pham (ed.), Reliability and Maintainability Assessment of Industrial Systems, pages 329-342, Springer.
    9. Singh, Ayush & Singh, S.B., 2025. "Dynamic reliability and sensitivity analysis of weighted (k, r)-out-of-n cold standby system with multi-performance multi-state components," Reliability Engineering and System Safety, Elsevier, vol. 262(C).
    10. Li, Wei & Zuo, Ming J., 2008. "Optimal design of multi-state weighted k-out-of-n systems based on component design," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1673-1681.
    11. Anatoly Lisnianski & Ilia Frenkel & Lev Khvatskin, 2021. "Modern Dynamic Reliability Analysis for Multi-state Systems," Springer Series in Reliability Engineering, Springer, number 978-3-030-52488-3, December.
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