Every broken appliance forces the same question, and retail flyers are not a neutral adviser. The honest framework fits in three numbers: the machine's age against its expected span, the repair quote against replacement cost, and the failure's category — wear part or core component.
The lifespan table, roughly

Refrigerators and gas ranges run 12-15 years; washers and electric ranges about 10-12; dishwashers and dryers 9-12. A machine in the front half of its span earns repairs; one past the finish line needs a special reason.
The 50 percent rule and its texture
Repair over half of replacement cost, on a machine past half its life: replace. But category matters — a dryer belt or fridge relay is a wear item worth doing at almost any age; a compressor or drum bearing on an aging unit is the machine announcing retirement.
Ask the tech what the part says about the rest of the machine. The good ones answer straight; it is why the diagnostic fee is information you keep either way.
Do not double-count features
Replacement only wins on energy if the old unit was a genuine hog — mostly pre-2010 refrigerators. New-machine premiums buy features, not longevity; entry-level replacements often live shorter lives than the repaired ten-year-old they replaced.
Local arithmetic
Springfield's hard water shortens dishwasher and washer spans a notch, which tilts borderline calls on those two toward replacement — while making the case for repairing solid older units built before wash motors got delicate. A tech who works Greene County water sees the difference weekly.
A fair way to use the diagnostic visit
Pay for the diagnosis, get the quote and the tech's read on the machine's remaining life, and decide with the three numbers in front of you. If replacement wins, you have lost only the diagnostic fee — and gained certainty you were not sold an appliance by a coupon.
Around here the machines worth fighting for are usually the pre-electronics workhorses; let the tech tell you which side of that line yours sits on.