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

Abstract

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.

DOI 10.5281/zenodo.17624255