You sound like you know this circuit.
Well, I have worked on similar type fridges. Weather it's the identical circuit is something else. Thinking back, I believe it used tranistors, F13005.
I have personally never seen a cap fail without some visual sign but how common is that?
Lucky you. It depends on the cap and manufacturer.
I don't know how many times I have removed caps on a whim only to learn that they are fine.
If your removing caps on a whim to test them then you do not have an ESR meter. Without An ESR meter you cannot properly check the caps 'quality'.
An ESR meter is the way to go. You can have a cap read proper uF with a basic cap meter but be defective by having a high internal resistance. An ESR meter does this and most times can be used with caps in circuit. Like everything it depends on circuit design.
If'n you do not have one , use a scope on the cap and look for ripple. If'n you don't have a scope, use a DVM on DC and AC volts. Have you measured this?
If the cap is failing, it will need to be replaced with a Low ESR type 105'C cap of equal quality. Regular joe blow cap will not work.. for long, if at all.
Also, you say "output caps", are you referring to the main power supply caps or the small caps in parallel with the output to the load?
Output caps are at the output
. Around 1000 uF around 16 to 25 volts.
Start by measuring the output and determining the manufacturer and series of the cap/s at the output. A nice pic of the boardwould help.
Cheers