Digital modeling of regulatory acts in industrial safety: quantitative assessment of applicability quality using hazard factor space and production locus

This study develops a set-theoretic digital framework for modeling regulatory acts and quantitatively assessing their applicability quality in industrial safety. Traditional regulations are treated as immutable rules, yet their reliability is often compromised by uncertainties in input data and variations in operating conditions. To address this limitation, industrial facilities are represented as points (or loci) in a multidimensional hazard factor space. Using R-functions, the regulatory algorithm is formalized as a single scalar function that defines the boundary between hazardous and safe regions. Proximity to this boundary forms an uncertainty region where regulatory decisions become unreliable.The applicability quality of a regulatory act is evaluated using three complementary criteria: (1) affiliation to and position within the uncertainty region, (2) magnitude of the hazard criterion, and (3) distance to the hazardous–safe boundary. The concept of a production area (including areas of danger, safety and uncertainty) is introduced, which allows for a quantitative characterization of the inherent safety, which is traditionally assessed only qualitatively. The structure of the production locus serves as an integral indicator of how well the regulatory act performs under real-world uncertainty.The proposed approach provides a foundation for developing digital twins of normative regulation systems and supports the transition from prescriptive to performance-based safety governance. Numerical examples with flammable gases and garage fire-load categorization demonstrate the practical applicability of the method. The framework is universal and can be extended to any algorithmic regulatory system.