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 based on the Reich model have been developed and applied to several practical cases.

A Japanese oceanic air traffic control system based on Automatic Dependent Surveillance (ADS) displays interpolated aircraft positions using the information on the down-linked present position and predicted future position (based on the estimated average speed and elapsed time to the next reporting position) of aircraft. In this system, the interpolation errors increase with the elapsed time from the latest reported time. The longitudinal collision risk estimation for the oceanic airspace under the ADS environment is of our great concerns. The longitudinal overlap probability is one of the key parameters of a longitudinal collision risk model. It depends upon the distribution shape of the position estimation (interpolation) errors. When considering the longitudinal collision risk for aircraft pairs, in general, the case where the effects of the interpolation errors on the relative position estimation errors become maximal has been assumed as the worst case. In this case, it has been believed that the case of the simultaneous reporting is the most conservative.

Recently, the empirical distribution of the ADS along-track position prediction (estimation) errors observed in the North Pacific showed the bias and non-symmetric shape. In this case, the assumption of the simultaneous reporting might not be valid for the case where the interpolation error distribution has a non-zero bias. This paper examines the validity of the assumption of the simultaneous reporting from the viewpoint of longitudinal overlap probability using a double exponential distribution model with a bias. The results of the analyses indicated that the assumption was not necessarily valid for the case. This paper also discusses the effects of ADS along-track position estimation errors on the longitudinal collision risk for aircraft flying in the airspace under consideration.