Reliability and launching policy for a system of satellites

The reliability of a system of satellites in which a number of satellites are launched at intervals is analyzed. The system is considered operational if at least one satellite in orbit is functioning. Analytical methods were investigated for determining a launching policy which would optimize some suitable system reliability parameter, but only a near-optimal policy could be found. The equations derived provide expressions for the reliability and mean downtime of the system within each time interval between successive launches and throughout the mission. The reliability model which was used included redundancy within the satellite, a launch success probability, and a satellite cut-off time (or end of life) due to fuel exhaustion.