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

Area of Science:

• Risk Management
• Statistical Modeling
• Reliability Engineering

Background:

• Traditional Failure Mode and Effects Analysis (FMEA) risk priority number (RPN) calculations assume independence between severity, occurrence, and detection scores.
• This assumption limits the accuracy and realism of risk assessments in complex systems.

Purpose of the Study:

• To introduce a novel probability model for FMEA RPN that addresses the limitations of traditional methods.
• To capture inherent dependencies among FMEA risk components using a Bayesian framework.

Main Methods:

• Development of a new probability model for FMEA RPN using sufficient statistics within a Bayesian framework.
• Validation through simulation studies assessing estimator accuracy and stability.
• Empirical analysis on AI risk assessment and gas refinery fire risk data.

Main Results:

• The proposed Bayesian model demonstrates superior accuracy and stability compared to traditional methods.
• Empirical analyses confirm the model's effectiveness and adaptability across diverse domains and sampling strategies.
• Model comparisons using p-values and AIC confirm the new model as the best fit for categorical risk data.

Conclusions:

• The new FMEA RPN model enhances the reliability and interpretability of risk assessments.
• It provides a more realistic and flexible representation of risk by accounting for component dependencies.
• This model serves as a powerful tool for decision-making and risk mitigation in safety-critical systems.