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The risk priority number (RPN) calculation method is one of the critical subjects of failure mode and effects analysis (FMEA) research. Recently, RPN research under a fuzzy uncertainty environment has become a hot topic. Accordingly, increasing studies have ignored the important impact of the random sampling uncertainty in the FMEA assessment. In this study, a fuzzy beta-binomial RPN evaluation method is proposed by integrating fuzzy theory, Bayesian statistical inference, and the beta-binomial distribution. This model can effectively realize real-time, dynamic, and long-term evaluation of RPN under the condition of continuous knowledge accumulation. The major contribution of the proposed model is to use the random uncertainty and fuzzy uncertainty in an integrated model and provide a Markov Chain Monte Carlo (MCMC) method to solve the complex integrated model. The study presented a case study, which presented how to apply this model in practice and indicated the significant influence on the measurement error caused by ignoring the random uncertainty caused by expert evaluation in RPN calculations.

The Risk Priority Number Evaluation of FMEA Analysis Based on Random Uncertainty and Fuzzy Uncertainty