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Computing system signatures through reliability functions

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  • Marichal, Jean-Luc
  • Mathonet, Pierre

Abstract

For a system with i.i.d. component lifetimes the Samaniego signature can be computed for instance from Boland’s formula, which requires the knowledge of every value of the associated structure function. We show how the signature can be computed more efficiently from the diagonal section of the reliability function via derivatives.

Suggested Citation

  • Marichal, Jean-Luc & Mathonet, Pierre, 2013. "Computing system signatures through reliability functions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 710-717.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:710-717
    DOI: 10.1016/j.spl.2012.11.018
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    References listed on IDEAS

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    1. Marichal, Jean-Luc & Mathonet, Pierre & Waldhauser, Tamás, 2011. "On signature-based expressions of system reliability," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1410-1416, November.
    2. Marichal, Jean-Luc & Mathonet, Pierre, 2013. "On the extensions of Barlow–Proschan importance index and system signature to dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 48-56.
    3. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    4. Marichal, Jean-Luc & Mathonet, Pierre, 2011. "Extensions of system signatures to dependent lifetimes: Explicit expressions and interpretations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 931-936, May.
    5. 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.
    6. 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, February.
    7. Barlow, Richard E. & Proschan, Frank, 1975. "Importance of system components and fault tree events," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 153-173, April.
    8. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
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    Cited by:

    1. Akshay Kumar & Subhi Tyagi & Mangey Ram, 0. "Signature of bridge structure using universal generating function," 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. 0, pages 1-5.
    2. 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.
    3. Akshay Kumar & Subhi Tyagi & Mangey Ram, 2021. "Signature of bridge structure using universal generating function," 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. 12(1), pages 53-57, February.
    4. 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.
    5. He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2022. "On Dependent Multi-State Semi-Coherent Systems Based on Multi-State Joint Signature," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1717-1734, September.
    6. 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.
    7. Sadiya Naaz & Rashmi Khanna & Riya Rawat & Neha Negi & Mangey Ram & Akshay Kumar & Anuj Kumar, 2024. "Signature reliability analysis of complex consecutive k-out-of-n:W CMO system via UGF and SFA," Journal of Risk and Reliability, , vol. 238(5), pages 1037-1052, October.
    8. 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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