Start with the failure, not the birthday
A refrigerator that is 12 or 15 years old is not automatically finished. A five-year-old refrigerator is not automatically worth repairing either. The decision starts with what failed, what the repair will cost, whether the rest of the machine is sound and what a suitable replacement would cost installed.
Get a diagnosis before using a percentage rule. A door gasket, fan or control problem is a different decision from a sealed-system failure. Ask the technician what failed, what else looks worn and whether the quoted repair carries a parts-and-labor warranty.
Energy savings usually are not enough by themselves
ENERGY STAR says certified refrigerators are about 9% more efficient than models that merely meet the federal minimum, and that replacing and properly recycling an old refrigerator with an ENERGY STAR model can save roughly $150 over a 12-year product life. That is useful, but it is not a reason to discard a working refrigerator just to chase the utility savings.
Very old units can be a different case. ENERGY STAR notes refrigerators over 15 years old can cost materially more to run. Use your electricity rate and an estimate of the old unit's consumption if energy cost is going to influence the decision.
Run the repair-life calculation
Suppose the repair is $450 and a comparable replacement is $1,500 after delivery, haul-away and any installation costs. If the repair plausibly buys three more years, you are paying about $150 per additional year of service. If it is likely to buy only one uncertain year, replacement becomes easier to justify.
Now add the costs that differ: expected electricity, food-loss risk if the unit is unreliable, and any features you genuinely need. Do not count features you would not have paid for before walking into the showroom.
When replacement becomes easier to defend
Replacement becomes more compelling when the repair is expensive, the refrigerator has had repeated failures, parts are difficult to obtain, temperatures are unstable, or the cabinet and door seals have deteriorated along with the failed component. A single inexpensive repair on an otherwise sound unit points the other way.
If the refrigerator is still cooling safely while you decide, take enough time to price a comparable replacement. Urgency is expensive. The goal is not to make an old appliance last forever; it is to avoid paying replacement price when a sensible repair still has value.