Alot of manufacturers provide a MTBF in hours. For instance, my last PSU had a MTBF of 100,000 hours, or 11 years of continous use.
That said, depending on the build quality of the PSU, the unit is more or less likely to degrade over time. The reason your PSU is not the piece of hardware to save money on is because when a PSU fails, they have a reputation to destroy other system components when they go out. So, saving 80$ by not buying a new PSU could potentially result in 400$ worth of dead motherboard and CPU.
If your unit is made with solid capacitors from a reputable company, it may be relatively "safe" to continue and use it. I personally upgraded my PSU after about 5-6 years, and kept the old one just in case I have any problems.