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Block diagram method for analyzing multi-state systems with uncovered failures

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  • Levitin, Gregory

Abstract

The paper suggests a modification of the generalized reliability block diagram (RBD) method for evaluating reliability and performance indices of multi-state systems with uncovered failures. Such systems (or their subsystems) can fail to perform their task in the case of undetected failure of any one of their elements. Examples of this effect can be found in computing systems, electrical power distribution networks, pipe lines carrying dangerous materials etc. The suggested method based on a universal generating function technique allows performance distribution of complex multi-state series-parallel system with uncovered failures to be obtained using a straightforward recursive procedure. Illustrative examples are presented.

Suggested Citation

  • Levitin, Gregory, 2007. "Block diagram method for analyzing multi-state systems with uncovered failures," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 727-734.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:6:p:727-734
    DOI: 10.1016/j.ress.2006.02.009
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    1. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, February.
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    Cited by:

    1. Levitin, Gregory & Xing, Liudong & Ben-Haim, Hanoch & Dai, Yuanshun, 2011. "Multi-state systems with selective propagated failures and imperfect individual and group protections," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1657-1666.
    2. Cao, Yingsai & Liu, Sifeng & Fang, Zhigeng & Dong, Wenjie, 2020. "Modeling ageing effects for multi-state systems with multiple components subject to competing and dependent failure processes," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    3. Schäfer, Lukas & García, Sergio & Srithammavanh, Vassili, 2018. "Simplification of inclusion–exclusion on intersections of unions with application to network systems reliability," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 23-33.
    4. Macchi, Marco & Kristjanpoller, Fredy & Garetti, Marco & Arata, Adolfo & Fumagalli, Luca, 2012. "Introducing buffer inventories in the RBD analysis of process production systems," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 84-95.
    5. Macchi, Marco & Garetti, Marco & Centrone, Domenico & Fumagalli, Luca & Piero Pavirani, Gian, 2012. "Maintenance management of railway infrastructures based on reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 71-83.
    6. Levitin, Gregory & Amari, Suprasad V., 2008. "Multi-state systems with multi-fault coverage," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1730-1739.
    7. G Levitin & S V Amari, 2008. "Multistate systems with static performance- dependent fault coverage," Journal of Risk and Reliability, , vol. 222(2), pages 95-103, June.
    8. Emmers, Glenn & Van Acker, Tom & Driesen, Johan, 2024. "A semi-Markovian approach to evaluate the availability of low voltage direct current systems with integrated battery storage," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    9. Levitin, Gregory & Xing, Liudong, 2010. "Reliability and performance of multi-state systems with propagated failures having selective effect," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 655-661.
    10. Wenzel, Lars & Wolf, André, 2013. "Protection against major catastrophes: An economic perspective," HWWI Research Papers 137, Hamburg Institute of International Economics (HWWI).
    11. Tazi, Nacef & Châtelet, Eric & Bouzidi, Youcef, 2018. "How combined performance and propagation of failure dependencies affect the reliability of a MSS," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 531-541.
    12. 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.

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