If the voltages are right, then it is safe to continue using the tube - nothing "fixable" has gone wrong.
That said, there are a lot of ways a tube can make a sporadic noise voltage, and a lot of kinds of such noise. Since this moves with the tube, you can get rid of it by replacing the tube - they are pretty cheap.
If you have an intellectual curiosity about what exactly causes this, you can probably get years of enjoyment hunting it down, and learn a ton of interesting tube trivia in the process. To get others usefully involved, you'd probably want to get a recording of the noise - descriptions are nearly impossible to make sense of, in spite of years spent by the audiophile press ... :^) Next step would be to see if you can identify something that triggers it - mechanical jostling, electrical environment (fridge coming on for example), certain musical events, anything or even nothing.