I would like to assess a system disponibility using a Markov Process. This system has two states : a functionning state 0 and a failure state 1, with a fault rate $\lambda$ and a mean time to repair MTTR = $1/\mu$.
My problem is that this system features a protection device wich can reduce the impact of a failure (and thus the amount of time needed to fix it), but this device can fail with a probability $\gamma$ when a fault occurs (a bit like if the event was triggered when a transition occurs from the functionning state to the failure state, like a circuit breaker for instance).
How can I take that kind of "instantaneous" event, triggered when a fault occurs, into account ?