It is more along the lines that you need to keep an eye on them while you are at the computer (have the program up and visible if possible). Additionally you can place the computer under load without needing to actually play a game via stress test programs such as Prime 95 (for CPU stress testing) and Furmark (for GPU/CPU/RAM stress testing). A couple other things you can do via Windows itself is run a RAM diagnostic to see if there is any errors that occur and possibly even run a check disk on the hard drive via system tools. If you are seeing actual errors in your Event log, try to get the event ID as well to help narrow the problem down as this could be caused by a bad registry setting, corrupt driver, or conflicting drivers as well.

There can be various reasons why you have a random shutdown, program crash, or blue screen errors (though you have not mentioned having any of these), but in order to help you beyond what others have suggested already it requires you take some additional steps to try an narrow the cause.