In lateral force resisting systems, fuses enable expedient repair while ensuring ductile system response. A bracing system is explored herein, in which hollow rectangular sections (RHS) and double channel sections (UPN) are used as the energy dissipating mechanism. Analyzed members have the same Eurocode section class (1st) and elastic section modulus. Loading on these fuses is a combination of bending moment, axial and shear loads (M−N−V). An analytical model is developed based on the Huber-Mises criterion to analytically describe the interaction between (M−N−V). The accuracy of the analytical model is benchmarked by a comparison with results of an experimental campaign and obtained through a finite element numerical model. The paper continues with a sensitivity analysis of the ultimate moment to the variation in axial and shear force. The analytical model is then adopted to assess how the fuse response is affected by the randomness in the design parameters (the geometrical features and mechanical properties). The impact of statistical variation in design parameters is elucidated through a Monte Carlo simulation. Variability in member geometric features was determined from current design specifications, while variability in steel mechanical properties was determined via experimental testing. The work concludes with an analysis and discussion of the Monte Carlo simulation with recommendations for designers and fabricators to encourage higher quality control in manufacturing. Variability in steel yield strength was found to have the most significant impact on the brace structural response, and must be tightly controlled for to produce accurate designs.