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Balanced reliability systems under Markov processes

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  • Lirong Cui
  • Jianhui Chen
  • Xiangchen Li

Abstract

Research on reliability for balanced systems has become an important issue in the reliability field; it is being intensively studied both in theory and applications. The concept of balance has many implications, which results in various balanced systems needing to be studied in reliability modelling, analysis and optimization and so on. In the present article, two balanced reliability systems are introduced and their reliability models are developed, then formulas for system reliability, probability density functions, and moments of lifetimes under two models are obtained using the results in aggregated stochastic processes or phase-type distributions for two-dimensional and high-dimensional situations. In addition, a matrix operator, the Kronecker product operator, is used to create concise forms for the related formulas. An algorithm for computing these reliability indexes is given to facilitate use. Some examples including symbolic and numerical ones for the simplest case, the two-dimensional situation, are shown to illustrate the presented results. The presented work may shed light on future research on reliability and safety for balanced systems under different concepts of balance.

Suggested Citation

  • Lirong Cui & Jianhui Chen & Xiangchen Li, 2019. "Balanced reliability systems under Markov processes," IISE Transactions, Taylor & Francis Journals, vol. 51(9), pages 1025-1035, September.
    • Handle: RePEc:taf:uiiexx:v:51:y:2019:i:9:p:1025-1035
    DOI: 10.1080/24725854.2018.1536304
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    Citations

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    Cited by:

    1. Wang, Xiaoyue & Ning, Ru & Zhao, Xian & Wu, Congshan, 2023. "Reliability assessments for two types of balanced systems with multi-state protective devices," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    2. Wang, Xiaoyue & Ning, Ru & Zhao, Xian & Zhou, Jian, 2022. "Reliability analyses of k-out-of-n: F capability-balanced systems in a multi-source shock environment," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    3. Fang, Chen & Cui, Lirong, 2020. "Reliability analysis for balanced engine systems with m sectors by considering start-up probability," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    4. Fang, Chen & Cui, Lirong, 2021. "Balanced Systems by Considering Multi-state Competing Risks Under Degradation Processes," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    5. Wang, Xiaoyue & Zhao, Xian & Wang, Siqi & Sun, Leping, 2020. "Reliability and maintenance for performance-balanced systems operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    6. Fang, Chen & Cui, Lirong, 2021. "Reliability evaluation for balanced systems with auto-balancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    7. Xu, Dong & Tian, Yubin & Shi, Junbiao & Wang, Dianpeng & Zhang, Ming & Li, Haijin, 2023. "Reliability analysis and optimal redundancy for a satellite power supply system based on a new dynamic k-out-of-n: G model," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    8. Yanbo Song & Xiaoyue Wang, 2022. "Reliability Analysis of the Multi-State k -out-of- n : F Systems with Multiple Operation Mechanisms," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    9. Yangyao, Shi & Xinchen, Zhuang & Tianxiang, Yu & Zijian, Zhang, 2023. "Multi-state balance system reliability research considering load influence," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    10. Wu, Bei & Cui, Lirong & Fang, Chen, 2020. "Multi-state balanced systems with multiple failure criteria," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    11. Wang, Siqi & Zhao, Xian & Wu, Congshan & Wang, Xiaoyue, 2023. "Joint optimization of multi-stage component reassignment and preventive maintenance for balanced systems considering imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    12. Wu, Congshan & Zhao, Xian & Wang, Xiaoyue & Wang, Siqi, 2021. "Reliability analysis of performance-based balanced systems with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    13. Wu, Congshan & Zhao, Xian & Wang, Siqi & Song, Yanbo, 2022. "Reliability analysis of consecutive-k-out-of-r-from-n subsystems: F balanced systems with load sharing," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    14. Wang, Siqi & Zhao, Xian & Tian, Zhigang & Zuo, Ming J., 2021. "Optimum component reassignment for balanced systems with multi-state components operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

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