A system consists of two machines, of which one works and the other is standby. Only the working machine can break down (with rate $\lambda$). If it breaks down the other machine takes over (if it not defect). The defect machine goes to a repairman, who repairs it at a rate $\mu$. After repair it is used as standby or put to work in case the other machine is defect. The repairman can only fix one machine at a time.
$\rightarrow$ Model as a continuous time Markov Chain. Draw a transition diagram, and give transitions rates.
My approach: Let $\{(X(t), Y(t): \ t \geq 0)\}$ be the state, where $X(t)$ denotes the number of working machines and $Y(t)$ the number of machines in repair. Then for $X(t)$ the transition rates are $q_{i, \ i+1}=\mu$ and $q_{i, \ i-1}=\lambda$. For $Y(t)$, $q_{i, \ i+1}=\lambda$ and $q_{i, \ i-1}=\mu$.
I don't think that's right though, as it is not necessarily so that a machine goes to the repairman if it breaks down for instance (as he could be busy). Also, I defined transition probabilities separately for $X(t)$ and $Y(t)$ which is probably wrong. Could anyone please show me how it should be done?