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All Journal Indonesian Journal of Applied Mathematics
Ekhlas Annon Mousa
Department of Mathematics, Ministry of Education, Babylon, Iraq
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Physics

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Reliability Analysis of Complex Systems: An Improved Risk Importance Measure Approach Ekhlas Annon Mousa; Ahmed Hasan Alridha
Indonesian Journal of Applied Mathematics Vol. 6 No. 1 (2026): Indonesian Journal of Applied Mathematics Vol. 6 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v6i1.2736

Abstract

This paper develops a new feature of the risk achievement worth (RAW) measure to expand its application to complex transportation directed networks, rather than being limited to traditional or undirected networks. The idea is to combine the RAW measure with modern techniques using the NetworkX library in Python, to improve its computational capabilities and handle complex directed networks efficiently. The approach was applied to a complex system . We calculated its reliability using a polynomial approach based on minimal paths and minimal cut sets, in addition to calculating the probability of path success and the probability of failure for cut sets. To demonstrate the effectiveness of the risk achievement worth measure, it was compared with the Birnbaum measures for analyzing the importance of network components at a default value of R = 0.60. The results showed complete consistency in terms of the importance levels of both measures, as confirmed by the Spearman correlation coefficient, with a value . Developing the risk achievement worth for analyzing complex networks is crucial to overcoming the computational complexity of the Birnbaum measure, which relies on differentials, unlike the RAW measure, which relies on simplified arithmetic procedures independent of differentials. Therefore, this provides an enables rapid identification of critical vulnerabilities in large-scale infrastructures.
Co-Authors Ahmed Hasan Alridha