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Study of Dynamic Solutions for Human–Machine System with Human Error and Common-Cause Failure

Author

Listed:
  • Juan Zhao

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China)

  • Ehmet Kasim

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China)

Abstract

This work investigates a dynamic solution of human–machine systems with human error and common-cause failure. By means of functional analysis, it is proved that the semigroup generated by the underlying operator converges exponentially to a projection operator by analyzing the spectral property of the underlying operator, and the asymptotic expressions of the system’s time-dependent solutions are presented. We also provide numerical examples to illustrate the effects of different parameters on the system and the theoretical analysis’s validity.

Suggested Citation

  • Juan Zhao & Ehmet Kasim, 2023. "Study of Dynamic Solutions for Human–Machine System with Human Error and Common-Cause Failure," Mathematics, MDPI, vol. 11(12), pages 1-29, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2771-:d:1174704
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    References listed on IDEAS

    as
    1. Asadzadeh, S.M. & Azadeh, A., 2014. "An integrated systemic model for optimization of condition-based maintenance with human error," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 117-131.
    2. Mohammed A. Hajeeh, 2011. "Availability of deteriorated system with inspection subject to common-cause failure and human error," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 12(2), pages 207-222.
    3. Jinting Wang & Nan Xie & Nan Yang, 2021. "Reliability analysis of a two-dissimilar-unit warm standby repairable system with priority in use," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(4), pages 792-814, February.
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