A simple algorithm for the system reliability in the 1-out-of-n system with exponential repair times

Consider a reliability model with one operating unit and n-1 warm standby units. The unit lifetimes during operation have a general probability distribution, while the lifetimes during warm standby are exponentially distributed. The units are repairable and have exponentially distributed repair times. There are ample repair facilities, so all failed units can be repaired simultaneously. For this model we give a recursive method to calculate the moments of the Time to System Failure. We use these moments to approximate the reliability probability distribution function by a sum of exponential functions. Based on numerical results we advise to use the first three moments of the Time to System Failure for the distribution approximation. Furthermore the sensitivity of the Mean Time to System Failure to the shape of the unit lifetime and the unit repair time distribution is studied. We conclude that the shape of the unit lifetime distribution affects the Mean Time to System Failure strongly. The shape of the unit repair time distribution has clearly less influence on the Mean Time to System Failure