Acceptable speaker hum from integrated or sign of impending failure?

I have two integrated amps that are now about a decade old and one produces a slight 60 Hz hum that is audible < 6 inches from speakers when power is on and no inputs are connected- the other is dead silent. The hum doesn't increase in volume as the knob is turned and is constant. I've moved the "hummer" to different circuits and no matter where it is plugged in or what is plugged into the inputs or outputs the hum is audible. Also tried swapping the three prong cords between the amps and this has no effect. Only had it a week or so and am not sure whether the hum is new or was unnoticed previously. Is this an acceptable shortcoming? My main concern is whether the power supply or any internals may be going bad and causing the hum.  Any thoughts greatly appreciated!
It could be a number of things, but two that I think of immediately are the power electrolytics (capacitors) or the rectifier. Both smooth out 60 Hz from the wall and could be the culprit. This is an easy fix. 
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Thanks so much for the responses:

@mental That seems like a very easy fix- will certainly try that first. Do you run through a power strip or GFI of some sort? Not sure if that would make the amp more susceptible to surges or other fluctuations.

@stevecham I will try googling those terms as I am electrically illiterate. When you say 'This is an easy fix' do you mean replacing those components?

@mental I have an extension chord that accepts three prong cords but is itself ungrounded/two prong. I ran the receiver through this with no audible change in the hum.

Not sure if this means anything but the speaker hum is audible once I switch on power at the rear of the amp (is this sending current to the transformer?) and gets very minutely louder when I turn off the standby mode it immediately powers into. More power = more hum? Also, now that its quieter in my space I can convey that the hum is most noticeable at a distance of between 3 and 6 inches but is still easily perceptible at 12", significantly less at 24", and inaudible at 36". Grateful for any other thoughts.
often the hum is caused by a transformer which has loosened and starts vibrating--i've cured it by opening the chassis and screwing down the transformer (make sure you keep the unit unplugged for a day or so before you do so). if it's some sort of group loop, you can also try a group isolator, which is a plug that goes between the ac receptacle and the power cord
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@loomisjohnson Would that be true for a hum audible in the connected speakers or within the chassis of the amplifier itself? If the former, then I will certainly give that a go.

my guess is that if it's audible within the chassis that it's more likely a problem with the internals of the unit itself (loose transformer, failing power supply, caps, etc.) than with the  ground or power, but it could be a number of things. i certainly don't see any harm in tightening the torroidal transformer before moving onto other causes. be careful
Unacceptable to me.   I can put my ear to my speaker with volume up and no hum at all.  Send it back to the manufacturer
@loomisjohnson Sorry, meant to say that the hum is not coming from the chassis, but the speakers only. Will leave unplugged and see about taking apart tomorrow.

@stringreen Unfortunately I am not the original owner and can't imagine that the unit is covered under warranty. Having the hardest time getting in touch with Simaudio anyway...
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