The paper considers a system subject to failure which is monitored by a periodic inspection/renewal policy. Two different inspection/renewal policies are considered. Under policy

$A$ the system is renewed in each inspection point. If there is no failure the renewal is instantaneously, if there is a failure the renewal takes a constant time. Under policy

$B$ the system remains unchanged in an inspection point if no failure has occurred and is renewed if there is a failure. The time for a renewal is assumed to be a multiple of the inspection interval. For both policies the system availability and the limiting average availability are derived. The results are illustrated by assuming an exponential and gamma-distributed lifetimes of the system.