See it used here: http://en.wikipedia.org/wiki/Fed-batch. In the table giving the different strategies to control growth in a fed-batch culture, one finds, for example: "on-line measurement of glucose". What does it mean? Is there an off-line meassurement? What does it mean?
Offline is used for things that are taken out of the reactor, or removed from the process.
Thus it's "on" or "off" the system depending on whether it's contained within the normal piping/fludics of the system: "On" is in the system, "Off" is out of the system.