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On computing signatures of coherent systems

Author

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  • Da, Gaofeng
  • Zheng, Ben
  • Hu, Taizhong

Abstract

It is difficult to compute the signature of a coherent system with a large number of components. This paper derives two basic formulas for computing the signature of a system which can be decomposed into two subsystems (modules). As an immediate application, we obtain the formula for computing the signature of systemwise redundancy in terms of the signatures of the original system and the backup one. The formula for computing the signature of a componentwise redundancy system is also derived. Some examples are given to illustrate the power of the main results.

Suggested Citation

  • Da, Gaofeng & Zheng, Ben & Hu, Taizhong, 2012. "On computing signatures of coherent systems," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 142-150, January.
    • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:142-150
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    References listed on IDEAS

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    1. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    2. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, April.
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    Cited by:

    1. Marichal, Jean-Luc & Mathonet, Pierre & Spizzichino, Fabio, 2015. "On modular decompositions of system signatures," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 19-32.
    2. Frank PA Coolen & Tahani Coolen-Maturi & Abdullah H Al-nefaiee, 2014. "Nonparametric predictive inference for system reliability using the survival signature," Journal of Risk and Reliability, , vol. 228(5), pages 437-448, October.
    3. Lili RONG & Peide LIU & Yanchang CHU, 2016. "Multiple Attribute Group Decision Making Methods Based on Intuitionistic Fuzzy Generalized Hamacher Aggregation Operator," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(2), pages 211-230.
    4. Abdullah H Al-nefaiee & Frank PA Coolen, 2013. "Nonparametric predictive inference for system failure time based on bounds for the signature," Journal of Risk and Reliability, , vol. 227(5), pages 513-522, October.
    5. Da, Gaofeng & Chan, Ping Shing & Xu, Maochao, 2018. "On the signature of complex system: A decomposed approach," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1115-1123.
    6. Leila Mohammadi, 2017. "The joint signature of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 566-579, October.
    7. Gaofeng Da & Lvyu Xia & Taizhong Hu, 2014. "On Computing Signatures of k-out-of-n Systems Consisting of Modules," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 223-233, March.
    8. Sadiya & Mangey Ram & Akshay Kumar, 2022. "A New Approach to Compute System Reliability with Three-Serially Linked Modules," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    9. Zarezadeh, S. & Mohammadi, L. & Balakrishnan, N., 2018. "On the joint signature of several coherent systems with some shared components," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1092-1100.
    10. Reed, Sean, 2017. "An efficient algorithm for exact computation of system and survival signatures using binary decision diagrams," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 257-267.
    11. Leila Mohammadi, 2017. "The joint signature of parallel systems for different permutations of failure times," Computational Statistics, Springer, vol. 32(4), pages 1727-1746, December.
    12. Qin, Jinlei & Coolen, Frank P.A., 2022. "Survival signature for reliability evaluation of a multi-state system with multi-state components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    13. He Yi & Lirong Cui, 2018. "A new computation method for signature: Markov process method," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(5), pages 410-426, August.
    14. Marichal, Jean-Luc & Mathonet, Pierre, 2013. "Computing system signatures through reliability functions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 710-717.
    15. Jia, Xujie & Shen, Jingyuan & Xu, Fanqi & Ma, Ruihong & Song, Xueying, 2019. "Modular decomposition signature for systems with sequential failure effect," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 435-444.

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