Probability Distribution of Risk Priority Numbers in Failure Mode and Effects Analysis

This study introduces a new probability model for the risk priority number (RPN) in Failure Mode and Effects Analysis (FMEA), addressing limitations of the traditional RPN calculation, which assumes independence among severity, occurrence, and detection scores. Leveraging sufficient statistics within a Bayesian framework, the proposed model captures the inherent dependencies among these components, providing a more realistic and flexible representation of risk. Simulation studies validate the estimator's superior accuracy and stability, while empirical analyses on both AI risk assessment and gas refinery fire risk data sets demonstrate its effectiveness and adaptability across diverse domains and sampling strategies. Model comparisons using p-values and the Akaike information criterion (AIC) confirm the new model as the best fit for categorical risk data, aligning naturally with our theoretical approach. The results suggest that this new model enhances the reliability and interpretability of FMEA risk assessments, providing a powerful tool for decision making and risk mitigation in complex safety-critical systems.