On the steady state unavailability of standby systems

In this paper we study the steady state unavailability of standby systems comprising n identical components of which n − 1 are normally operating and one is in standby, with one repair facility. The components are assumed to have constant failure rates, but arbitrary repair time distribution. Attention is given to the case that the mean time to repair MTTR is relatively small compared to the mean time to failure MTTF, which is the most common situation in practice. Simple approximation formulae are presented and compared with the standard Markov expressions. It is demonstrated that the Markov expressions produce relatively large errors when the coefficient of variation of the repair time distribution is not close to 1. Some easily computed error bounds of the approximation formulae are established.