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Estimating the reliability of complex systems using various bounds methods

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  • Emad Kareem Mutar

    (Directorate of Education Babylon)

Abstract

The precise two-terminal reliability calculation becomes more difficult when the numeral of components of the complex system increases. The accuracy of approximation methods is often adequate for expansive coverage of practical applications, while the algorithms and computation time are typically simplified. As a result, the reliability bounds of two-terminal systems and estimation methods have been established. Our method for determining a complex system's reliability lower and upper bounds employs a set of minimal paths and cuts. This paper aims to present a modern assessment of reliability bounds for coherent binary systems and a comparison of various reliability bounds in terms of subjective, mathematical, and efficiency factors. We performed the suggested methods in Mathematica and approximated their interpretation with existing ones. The observed results illustrate that the proposed Linear and Quadratic bounds (LQb) constraint is superior to Esary-Proschan (EPb), Spross (Sb), and Edge-Packing (EDb) bounds in the lower bond, and the EDb bound is preferable to other methods above in the upper bond. This modification is attributed to sidestepping certain duplicative estimations that are part of the current methods. Given component test data, the new measure supplies close point bounds for the system reliability estimation. The Safety–Critical-System (SCS) uses an illustrative model to show the reliability designer when to implement certain constraints. The numerical results demonstrate that the proposed methods are computationally feasible, reasonably precise, and considerably speedier than the previous algorithm version. Extensive testing on real-world networks revealed that it is impossible to enumerate all minimal paths or cuts, allowing one to derive precise bounds.

Suggested Citation

  • Emad Kareem Mutar, 2023. "Estimating the reliability of complex systems using various bounds methods," 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. 14(6), pages 2546-2558, December.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:6:d:10.1007_s13198-023-02108-7
    DOI: 10.1007/s13198-023-02108-7
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    References listed on IDEAS

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    1. Sebastio, Stefano & Trivedi, Kishor S. & Wang, Dazhi & Yin, Xiaoyan, 2014. "Fast computation of bounds for two-terminal network reliability," European Journal of Operational Research, Elsevier, vol. 238(3), pages 810-823.
    2. Emad Kareem Mutar & Gianpaolo Di Bona, 2022. "Analytical Method of Calculating Reliability Sensitivity for Space Capsule Life Support Systems," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-9, August.
    3. Esha Datta & Neeraj Kumar Goyal, 2017. "Sum of disjoint product approach for reliability evaluation of stochastic flow networks," 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. 8(2), pages 1734-1749, November.
    4. Esha Datta & Neeraj Goyal, 2023. "An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs," 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. 14(4), pages 1228-1246, August.
    5. S. C. Malik & S. K. Chauhan & Nitika Ahlawat, 2020. "Reliability analysis of a non series–parallel system of seven components with Weibull failure laws," 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. 11(3), pages 577-582, June.
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