Hybrid Fuzzy–Neutrosophic Weibull Stress–Strength Reliability Model with Simulation and Real Data Analysis

This work fills an important gap in the conventional stress-strength reliability analysis, which usually considers precise parameter values and thus neglects the existing uncertainty in practical engineering systems. To remedy this deficiency, a hybrid fuzzy-neutrosophic Weibull stress-strength reliability model is proposed, which considers the interval-valued scale parameters to model the parameter uncertainty and introduces a sensitivity parameter <img src=image/13444143_01.gif> for graded safety analysis. Thus, the proposed model provides interval-valued reliability estimates <img src=image/13444143_02.gif> that capture the uncertainty. With the help of jute fiber strength information and Monte Carlo simulation, the findings reveal that for strict safety requirements <img src=image/13444143_01.gif>=0.001, the fuzzy reliability is only 11.9%, whereas the classical value is 53.5%, and thus the classical approach may overestimate the reliability by about 4.5 times. Additionally, neutrosophic extension enables uncertainty-based reliability intervals, e.g., [0.0925, 0.1486], when <img src=image/13444143_01.gif> = 0.001, and the width of the interval (0.0561) quantifies the parameter uncertainty. Furthermore, a new three-tier decision strategy is proposed to interpret the interval estimates and provide accept, reject, and retest decisions. The main contributions of this work are the formulation of a new unified reliability model, which encompasses both fuzzy graded evaluation and neutrosophic parameter uncertainty, providing a more realistic and practical tool for engineers in safety-critical applications, e.g., medical devices and aerospace engineering. Furthermore, simulation results validate the statistical consistency and efficiency of the new reliability model, demonstrating a decrease in mean squared error (MSE) up to 95% as the sample size increases.