  We define a model of a system that deteriorate as a result of (i) shocks,
modeled as a compound Poisson process and (ii) deterministic, state dependent
progressive rate, with variable and fixed maintenance cost. We define
maintenance strategies based on an impulse control model where time and size of
interventions are executed according the the system state, which is obtained
from permanent monitoring. We characterize the value function as the unique
viscosity solution of the HJB equation and prove that a
$(\underline{s},\overline{s},S)$ policy is optimal. We also provide numerical
examples. Finally, a singular control problem is proposed when there is no
fixed cost, which study and relation with the former problem is open for future
discussion.
