The worst alarm radio I ever owned was a Pure model, Tempus? When I set it to come on at the start of the Today programme, at 6am, I expected it to switch on at 6am. Pure boasted about the time keeping of their radios, locked as they were to the time signal of FM broadcasts. What they neglected to mention was that
1 The time signal was only acquired when the radio came on.
2 There was no attempt to acquire the time maybe 15 minutes before the alarm time.
3 The old crock of a digital clock inside the radios was capable of losing or gaining up to 3 minutes in a day.