Mechanization and automation of the coal industry as well as increasing the government support for safety in coal mines in China resulted in a significant decrease in the death rate per million tons of coal produced. Nonetheless, major accidents still occur. As one of the five factors of safe production, safety investment plays a key role in ensuring the safe production of coal in mining enterprises. Coal mining enterprises can ensure safe production in the mines and maximize profits through optimum safety investment. In this study, safety system engineering principles and subsets in set theory were combined to develop a novel safety investment index system. The safety investment indices were categorized into human, machine, environment, and the intersection of these three indices. The elements in each investment set were examined, and a multivariate model of safety investment and accident control was created using gray forecasting theory. In addition, a case study was conducted to validate the reliability of the model. The results indicated that the proposed model can provide theoretical evidence and guidance for safety investment decision making in coal mining enterprises. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.