Consider a two-unit parallel system (i.e., the system operates if at least one unit is operating). The lifetimes of the units have an exponential distributions with parameter \(\lambda\). There is one repairman, who can only attend one failed unit at a time. Repairs times have an Erlang distribution with parameters \(n=2\) and \(\lambda=1 / 2\). The system arrives at the failed state as soon as a unit fails during the repair of the other one. All life and repair times are assumed to be independent.

(1) By using Erlang's phase method, determine the relevant state space of the system and draw the corresponding transition graph of the underlying Markov chain.

(2) Determine the stationary availability of the system.