Reliability and sensitivity analysis of consecutive k-out-of-r-from-n:F systems using trapezoidal neutrosophic numbers and UGF approach

Reliability analysis under uncertain, imprecise, and time-dependent conditions remains a critical challenge in system engineering, especially for complex configurations such as linear consecutive (LC) k-out of-r-from-n:F systems. Existing probabilistic and fuzzy models often fail to capture the combined effects of vagueness, indeterminacy, and dynamic failure behavior. To address this gap, the present study proposes an inte grated neutrosophic fuzzy reliability framework that employs trapezoidal neutrosophic fuzzy numbers (TrNFNs) with the universal generating function (UGF) technique for life-cycle reliability and sensitivity evaluation. The methodology incorporates the α,β,γ-cut approach to quantify uncertainty and applies Weibull and Pareto life time distributions to model time-dependent failure rates. Comparative results reveal that system reliability decreases over time but remains consistently higher under Pareto than Weibull distribution, indicating greater robustness for rare yet severe failure scenarios. A novel sensitivity of fuzzy reliability (SOFR) index is also developed to identify degradation intervals and optimize maintenance scheduling. The proposed TrNFN–UGF framework enhances neutrosophic reliability theory by integrating time-varying distributions with multidimen sional uncertainty representation. Its applicability to mission-critical domains such as aerospace, healthcare, and smart manufacturing demonstrates its potential as a practical decision-support tool for reliability prediction and maintenance planning under complex uncertainty environments.