The best way to see if the system is stable is to just use it as you normally would, and hope for the best.
Hi, Well as An Overclocker I have learned that using the Benchmarks like Intel Burn Test is a Good way to check a System for STABILITY..
Even if you are NOT Overclocking your Rig I would reccomend trying to use Intel Burn Test and run it for 10mins..
No Please Run a Temp Monitor when running the Intel Burn Test to monitor the CPU temps and make sure you do NOT go near the Limit of your CPU look on Intels Website and find out yout T Case Temp.. for example I have an i5 and the T Case Temp is 72.6C... But if you are NOT Overclocked it should go NO where near your limits.. but it will get a little bit hot..but fear not it is designed to do just that but this will test your system for stability.
If it Fails you know there is something wrong with your System..
I would also run a GPU Benchmark like FurMark to test the stability of your GPU..