This paper examines the availability of a maintained system where the
rate of deterioration is governed by an exogenous random environment.
We provide a qualitative result that exposes the relationship between
remaining lifetime, environment, and repairs. This result leads to sim
ple bounds that can be used to choose inspection rates that guarantee
a specified level of availability. The principal result requires no sp
ecific distributional assumptions, is intuitively appealing and can be
directly applied by practitioners. Our development employs techniques
from stochastic calculus.