In this paper collision threat parameters such as the distance at closest point of approach and time to the closest point of approach are derived and analysed for special cases and features; collision criteria are analysed for limitations. A new collision threat parameter - time to safe distance - is proposed and its different applications to collision avoidance are presented. Time to safe distance can replace time to the closest point of approach, as it gives a safer time in a dangerous situation. It can be applied in Automatic Radar Plotting Aids (ARPAs) to detect dangerous objects and to display possible evasive manoeuvres.