From observation to expectation: A bayesian approach to evaluating engineering control effectiveness for nanomaterial exposure

Abstract This study evaluates engineering control effectiveness for nanomaterials across diverse workplaces using a Bayesian framework that bridges theoretical performance and real-world protection. We assessed seven workplaces spanning laboratory, manufacturing, spray application, and disposal operations, measuring titanium dioxide and respirable dust at all sites, with particle number concentration monitoring at four locations. Our analysis employed three metrics: observed efficiency (E_obs), stability-adjusted efficiency (η_adj), and Bayesian-adjusted efficiency (η_Bayes), which integrates Exposure Control Efficacy Library (ECEL) benchmarks with field measurements. Results revealed substantial performance variation across settings. Laboratory environments showed moderate efficiencies (E_obs: 0.249–0.806). Manufacturing operations achieved high Bayesian values (η_Bayes: 0.750–0.986) yet fell below ECEL benchmarks. Spray applications demonstrated the widest performance range, with observed efficiencies (E_obs: 0.292–0.911) significantly exceeding stability-adjusted values (η_adj: 0.038–0.156). Our findings indicate control effectiveness depends on implementation quality, temporal stability, and process dynamics beyond control type. The stability factor proved critical in dynamic environments, where high initial efficiencies masked poor consistency (e.g., spray applications with E_obs ~ 0.91 undermined by S < 0.20). The ECEL-based Bayesian approach enables contextual performance assessment, revealing that similar efficiency values may satisfy expectations in one setting but not another. Future strategies should prioritize robust containment systems effective during transitional operations while implementing activity-specific protocols addressing both peak exposures and temporal variability.