Catalytic converters in sulfur recovery units (SRUs) play a vital role in ensuring efficient sulfur conversion and minimizing hazardous emissions, yet their specific failure modes remain largely understudied. Traditional failure mode and effects analysis-based risk assessment is constrained by equal criterion weighting and by its inability to concurrently address vagueness and the reliability of expert judgments. To address this methodological gap, this study introduces a novel framework that integrates Z-number Stepwise Weight Assessment Ratio Analysis (Z-SWARA) to determine fuzzy reliability-based weights for severity, occurrence, and detection criteria and Z-number Weighted Aggregated Sum Product Assessment (Z-WASPAS) to rank failure modes. This represents the application of this specific hybrid Z-number approach to SRU catalytic converters, explicitly capturing both uncertainty and expert confidence. Expert linguistic evaluations were converted into Z-numbers to construct a realistic weighted decision matrix evaluating 23 identified SRU risk modes. Based on the Z-SWARA results, severity emerged as the most critical criterion (weight = 0.420), followed by occurrence (0.325) and detection (0.256). Furthermore, the Z-WASPAS ranking revealed that the most critical risks are hot spot formation in the catalyst bed (K = 0.83), coke formation on the catalyst (K = 0.78), and malfunction of the inlet control valve (K = 0.77). The results demonstrate that the proposed hybrid approach significantly improves the discriminative power and accuracy of risk prioritization, supporting proactive maintenance and effective risk management in complex process facilities.