The way you've worded the question it seems to imply you are changing important parameters on a primary use system. I generally build it, test it, and after it's been tested only then would it be considered as a replacement for my primary use system.
If you just mean misc. upgrades to your already used primary system where it was already known stable except for one subsystem changing like memory, let Memtest86+ run overnight at 5% higher o'c than my target. Video, let 3Dmark and ATITool run while I'm away from the system doing something else. CPU, I don't usually upgrade CPUs anymore on the same motherboard, but again I'd start the test when I was ready to get up from using the system and about to go do something non-computer.
Basically it's not as though you could use the system for something else in cases like memtest86+ or 3Dmark looping, and in other testing you don't really want to use the system for something else because if there's task switching going on you may be causing the system to spend more time on a less stressful task which decreases the stressfulness of a stress test.