Mission Reliability for a 1-Unit System with Allowed Down-Time

This paper considers a 1-unit system; the unit is repaired upon failure. The failure and repair rates need not be constant. The system fails if the unit is not repaired within a fixed time, or if the number of failures during the mission exceeds a fixed number. As a special case, that number is allowed to be ``infinite.'' The Laplace transforms of the reliability and mean time to system failure are derived; they are not easily solved. The special case of constant failure and repair rates is treated. The results are compared with those of Calabro.