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Subsignatures of systems

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  • Marichal, Jean-Luc

Abstract

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow–Proschan importance index. Specifically, given a nonempty subset M of the set of components of a system, we define the M-signature of the system as the |M|-tuple whose kth coordinate is the probability that the kth failure among the components in M causes the system to fail. We give various explicit linear expressions for this probability in terms of the structure function and the distribution of the component lifetimes. We also examine the case of exchangeable lifetimes and the special case when M is a modular set.

Suggested Citation

  • Marichal, Jean-Luc, 2014. "Subsignatures of systems," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 226-236.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:226-236
    DOI: 10.1016/j.jmva.2013.11.002
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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. Iyer, Srinivas, 1992. "The Barlow-Proschan importance and its generalizations with dependent components," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 353-359, September.
    3. 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.
    4. 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, December.
    5. 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.
    6. 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.
    7. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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    1. Marichal, Jean-Luc, 2014. "Computing subsignatures of systems with exchangeable component lifetimes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 128-134.

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