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The structure function for system reliability as predictive (imprecise) probability

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  • Coolen, Frank P.A.
  • Coolen-Maturi, Tahani

Abstract

In system reliability, the structure function models functioning of a system for given states of its components. As such, it is typically a straightforward binary function which plays an essential role in reliability assessment, yet it has received remarkably little attention in its own right. We explore the structure function in more depth, considering in particular whether its generalization as a, possibly imprecise, probability can provide useful further tools for reliability assessment in case of uncertainty. In particular, we consider the structure function as a predictive (imprecise) probability, which enables uncertainty and indeterminacy about the next task the system has to perform to be taken into account. The recently introduced concept of ‘survival signature’ provides a useful summary of the structure function to simplify reliability assessment for systems with many components of multiple types. We also consider how the (imprecise) probabilistic structure function can be linked to the survival signature. We briefly discuss some related research topics towards implementation for large practical systems and networks, and we outline further possible generalizations.

Suggested Citation

  • Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2016. "The structure function for system reliability as predictive (imprecise) probability," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 180-187.
    • Handle: RePEc:eee:reensy:v:154:y:2016:i:c:p:180-187
    DOI: 10.1016/j.ress.2016.06.008
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    References listed on IDEAS

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    1. Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2015. "Predictive inference for system reliability after common-cause component failures," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 27-33.
    2. 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.
    3. 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.
    4. T Coolen-Maturi & F P A Coolen, 2011. "Unobserved, re-defined, unknown or removed failure modes in competing risks," Journal of Risk and Reliability, , vol. 225(4), pages 461-474, December.
    5. 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.
    6. F P A Coolen & A H Al-nefaiee, 2012. "Nonparametric predictive inference for failure times of systems with exchangeable components," Journal of Risk and Reliability, , vol. 226(3), pages 262-273, June.
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    Cited by:

    1. Huang, Xianzhen & Jin, Sujun & He, Xuefeng & He, David, 2019. "Reliability analysis of coherent systems subject to internal failures and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 75-83.
    2. Wang, Jian & Sun, Zhili & Cao, Runan, 2021. "An efficient and robust Kriging-based method for system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Chang, Miaoxin & Huang, Xianzhen & Coolen, Frank PA & Coolen-Maturi, Tahani, 2023. "New reliability model for complex systems based on stochastic processes and survival signature," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1349-1364.
    4. Coolen-Maturi, Tahani & Coolen, Frank P.A. & Balakrishnan, Narayanaswamy, 2021. "The joint survival signature of coherent systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    5. Hernandez-Perdomo, Elvis & Guney, Yilmaz & Rocco, Claudio M., 2019. "A reliability model for assessing corporate governance using machine learning techniques," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 220-231.
    6. Yuan, Kai & Xiao, Ning-Cong & Wang, Zhonglai & Shang, Kun, 2020. "System reliability analysis by combining structure function and active learning kriging model," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    7. Salomon, Julian & Winnewisser, Niklas & Wei, Pengfei & Broggi, Matteo & Beer, Michael, 2021. "Efficient reliability analysis of complex systems in consideration of imprecision," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Patelli, Edoardo & Feng, Geng & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2017. "Simulation methods for system reliability using the survival signature," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 327-337.
    9. Cui, L.X. & Du, Yi-Mu & Sun, C.P., 2023. "On system reliability for time-varying structure," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    10. Vaisman, Radislav & Sun, Yuting, 2021. "Reliability and importance measure analysis of networks with shared risk link groups," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    11. Xianzhen Huang & Frank PA Coolen, 2018. "Reliability sensitivity analysis of coherent systems based on survival signature," Journal of Risk and Reliability, , vol. 232(6), pages 627-634, December.

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