Reliability Modelling and Performance Evaluation of Active Parallel System with Interactions of Three Failure Types Using Copula Linguistic
DOI:
https://doi.org/10.70882/josrar.2026.v3i3.226Keywords:
Interaction, Parallel, Reliability, CopulaAbstract
This study presents a novel reliability modelling framework for a unit active parallel system subjected to three interacting failure types—minor, medium, and major—using a copula linguistic approach. Traditional reliability models often rely on the assumption of failure independence and binary operational states, which do not accurately reflect the complex failure interactions observed in real-world systems. To address this limitation, we integrate linguistic fuzzy logic with copula theory to capture the dependencies among heterogeneous failure modes while accommodating imprecise failure information. The proposed model accounts for component-level interactions, realistic repair strategies, and escalation pathways among failure types. Analytical expressions are derived for key performance metrics, including availability, mean time to failure (MTTF), and system downtime. Numerical evaluations and sensitivity analyses demonstrate the model’s robustness and practical relevance in identifying critical dependence structures and supporting maintenance decision-making. The approach provides a flexible, interpretable, and computationally viable solution for reliability assessment in safety-critical active parallel systems.
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Copyright (c) 2026 Kabiru Garba Ibrahim, Ibrahim Yusuf, Hamisu Ismail Ayagi, Abdullahi Sanusi (Author)
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