Mintu Kumar
Department of Sciences, Quantum University, Roorkee, Uttarakhand, India.

S. B. Singh
Department of Mathematics Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand, India.

Monika Manglik
Department of Mathematics, Applied Science Cluster, University of Petroleum and Energy Studies, Bidholi, Dehradun, Uttarakhand, India.

DOI https://doi.org/10.33889/IJMEMS.2025.10.2.030

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Abstract

In scenarios where system component failure probabilities are insufficient or imprecise, classical fault tree analysis methods often fail in providing precise assessments of system reliability and safety. This limitation arises because classical fault tree analysis relies on precise data and probabilistic measures, which may not adequately capture inherent uncertainties and vagueness in real-world environments. Therefore, a general approach is required to reliably predict and diagnose system failures that incorporates the uncertainties inherent in failure data. The fuzzy sets effectively manage imprecise information and serve as a robust foundation to address ambiguity in real-world failure scenarios. Additionally, the use of intuitionistic fuzzy sets further enhances this framework by considering both membership and non-membership degrees, thereby providing a more comprehensive and precise reliability assessment. Therefore, in the current study, the intuitionistic fuzzy set theory is proposed to handle the inherent uncertainty in reliability assessments. Furthermore, triangular intuitionistic fuzzy numbers are used to represent the failure probabilities of the system components. The proposed method integrates intuitionistic fuzzy set theory with fault tree analysis to determine the reliability and failure probability of a rope on a crane, and the computed results are compared with the results of existing methods.

Keywords- Fault tree, Coherent system, Intuitionistic fuzzy sets, Fuzzy failure probability, Fuzzy reliability.

Citation

Kumar, M., Singh, S. B., & Manglik, M. (2025). Failure Probability Analysis of Coherent Systems using Intuitionistic Fuzzy Fault Tree Approach. International Journal of Mathematical, Engineering and Management Sciences, 10(2), 583-597. https://doi.org/10.33889/IJMEMS.2025.10.2.030.