Availability and frequency of warm standby systems in the presence of chance with multiple critical errors

This paper presents the availability and frequency of encountering different state of k active, N warm standby units in the presence of chance with M multiple critical errors. The system is in a failed state when one of any multiple critical errors has occurred or when (N+1) units have failed. Failed units are not repaired. However, failed system will be repaired with constant repair rates. The expressions for steady-state availability and frequencies of down- and up-states are derived.