For groups, servers and sensors you can choose a dependency by selecting an item from the “dependency” dropdown. For groups all associated servers and for servers all associated sensors will inherit this dependency.
If a dependency is selected the sensor (or all sensors of the group or the server) will enter a PAUSED status (blue) as soon as the dependency sensor is not UP (green) and will not be monitored until the dependency sensor returns to the UP status.
This means that monitoring will be paused if the dependency sensor is in DOWN, WARNING or PAUSED state! This also the case if the dependency sensor is paused due to a schedule.