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Importance analysis of multi-state systems based on tools of logical differential calculus

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  • Kvassay, Miroslav
  • Zaitseva, Elena
  • Levashenko, Vitaly

Abstract

Importance analysis deals with the investigation of influence of individual system components on system operation. This investigation can be qualitative or quantitative. The qualitative analysis focuses on finding scenarios in which a degradation/improvement of a specific component or a group of components results in a degradation/improvement of the whole system, while the quantitative one deals with numerical estimation of components importance. In this paper, we propose a new approach for importance analysis of Multi-State Systems (MSSs). The qualitative or quantitative importance analysis is based on the identification of critical states. The new approach can be used for calculation of all types of critical states. It is based on the application of direct partial logic derivatives. These derivatives are one of the methods of logical differential calculus. In this paper, the specifics of these derivatives for importance analysis of MSSs are considered in detail.

Suggested Citation

  • Kvassay, Miroslav & Zaitseva, Elena & Levashenko, Vitaly, 2017. "Importance analysis of multi-state systems based on tools of logical differential calculus," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 302-316.
    • Handle: RePEc:eee:reensy:v:165:y:2017:i:c:p:302-316
    DOI: 10.1016/j.ress.2017.03.021
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    References listed on IDEAS

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    1. Cadini, F. & Santos, F. & Zio, E., 2014. "An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 109-117.
    2. Praks, Pavel & Kopustinskas, Vytis & Masera, Marcelo, 2015. "Probabilistic modelling of security of supply in gas networks and evaluation of new infrastructure," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 254-264.
    3. Feng, Geng & Patelli, Edoardo & Beer, Michael & Coolen, Frank P.A., 2016. "Imprecise system reliability and component importance based on survival signature," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 116-125.
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    Cited by:

    1. Eryilmaz, Serkan & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2018. "Marginal and joint reliability importance based on survival signature," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 118-128.
    2. Sedlacek, Peter & Zaitseva, Elena & Levashenko, Vitaly & Kvassay, Miroslav, 2021. "Critical state of non-coherent multi-state system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    3. Cao, Yingsai & Lu, Chen & Dong, Wenjie, 2024. "Importance measures for multi-state systems with multiple components under hierarchical dependences," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    4. Yaguang Wu & Qingan Qiu, 2022. "Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks," Mathematics, MDPI, vol. 10(15), pages 1-18, August.
    5. Zaitseva, Elena & Levashenko, Vitaly & Rabcan, Jan, 2023. "A new method for analysis of Multi-State systems based on Multi-valued decision diagram under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    6. Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Fan, Yu, 2020. "Multi-state balanced systems in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    7. Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Cai, Kui, 2018. "A multi-state shock model with mutative failure patterns," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 1-11.
    8. 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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