An n unit system with spares

This paper deals with a system consisting of(n+m)identical units;n units are needed for the system to function, while the remaining m units are warm standbys. The online and standby units have different constant failure rates. There is no facility for repair. When the system is down due to the failure of(m+1) units, the remaining units can also fail with a (different) constant failure rate. Functions expressing the probability that in (0,t) there are i online failures and j standby failures are obtained. © 1989.