A study of MTTF in two-unit standby redundant system with priority under limited information about failure and repair times

We consider a two-unit standby redundant system with priority. In the previous literature, the theoretical formulae for the MTTF of such a system have been obtained using the renewal theory in the condition that the probability distributions about failure and repair times have the respective explicit functions. However, it is sometimes impossible to calculate the MTTF of the system depending on the probability distributions in the case of using the theoretical formulae in the previous literature. In this paper, we consider the situation that the probability distributions about failure and repair times can be approximated as a mixed Erlang distribution. Under this situation, we develop a new approximation procedure for computing the MTTF of the system by combining some results of the Markov analysis based on Erlang distributions. Then, we investigate the validity of our proposed approximation by simulation.