International Civil Aviation Organization (ICAO) has been documenting the need for system safety management in air traffic services (ATS) systems. When we try to change a part of ATS systems or procedures associated with safety, we have to demonstrate that the proposed change in the systems would be safe against the predetermined safety objective. Therefore, the safety assessment is required prior to the implementation of the new system. Mathematical collision risk modeling is an approach for quantitative safety assessment. The Reich model is the one, which has been widely used for the determination of separation minima. Several collision risk models...