Reliability prediction for repairable redundant systems

It is assumed that the mean time to failure and mean repair time are known for each of the subsystems of a system. The subsystems conform to the usual exponential failure (and repair) laws and their behaviors are mutually independent. The system includes redundant subsystems in active standby status. Whenever, after a system failure, repair of a failed subsystem re-establishes an adequate configuration, the system as a whole is returned to active status while repair of other failed subsystems (if any) continues. Under this set of assumptions, equations are developed which permit prediction of mean time to failure and mean down time for the system. The development differs somewhat from the use of birth-and-death equations which has been customary for similar problems in the past.