Rich 300

Has anyone had probs with alternaters going duff ?

One day i notice a strange small beep from alarm when starting the car, every thing else seems ok, then a couple of days or so later car wont start, the alarm goes off when you try, the imobilzer i assume is stopping the car from starting. Put on a set of jump leads and all is good car starts, have put a voltmeter on alternater when running and getting readings of 11 volts or so.
I have had battery tested been told its good, changed alternaters and thought it was sorted now about 3 weeks later the alarm has started to make the small beep when starting again, just waiting for the time when it wont start to come around again.
Any pointers would be appreciated chaps