Bayesian Validation Framework for Multinomial Processes in Dynamic Systems

The validation of operational precision in safety-critical dynamic systems requires advanced statistical frameworks to address multidimensional performance characterization under limited test resources. This study proposes a Bayesian decision model integrated with Dempster-Shafer evidence theory, overcoming the limitations of traditional binomial validation methods through multinomial distribution-based zone classification. By defining six-tier precision metrics weighted by zonal criticality and synthesizing multi-source prior data (historical tests, simulation data, expert judgments), the framework achieves adaptive risk-balanced acceptance thresholds. Experimental validation using industrial robotic arm datasets demonstrates a 39.2% reduction in Type I/II error risks compared to conventional Neyman-Pearson methods, while maintaining real-time decision speeds below 1.2 seconds, providing a universal solution for high-stakes validation in automated manufacturing and medical device certification.