Approximation Formulas for Reliability with Repair

A system consists of n-identical parallel subsystems, each having an exponential distribution of times to failure and an exponential distribution of times to repair. The system reliability with repair is the probability of no more than q out of n subsystems being simultaneously in a failed state during time t. Under conditions frequently met in practice, system reliability with repair R(t) can be approximated by: R(t) ? exp ?t/Tm] where Tm is the mean time for the system to pass for the first time from zero to (q + 1) simultaneous subsystem failures. Exact and approximate methods of calculating Tm are developed. A detailed error analysis is presented showing the limitations of using Tm to calculate system reliability with repair.