I have seen some of the standards of how to test say 12v,48v system etc. Some of the tests say maintain over voltage for 3 secs, they specify the raise time etc. My doubts are how do they derive these test cases? If they mention overvoltage should be for some x. Does it mean that my system will not be exposed more than this time? Please advise.

 

Stress/overvoltage test conditions/values are somewhat arbitrary.
The typically are values greater than the system is expected to see during its normal operational lifetime.

 

But on what basis do they specify the time?

 

It's just used as a general reference of abuse. Over voltage can effect a component in two ways. The over voltage can cause an arc and immediate destruction. But it can also cause a rise in current, which causes a rise temperature.

In some circuits.....submarines and satellites, one wants great abuse ability, before failure.