You know really Axle stands are not that good for modern cars, It's actually hard enough to find good places to even jack FWD cars. Axel stands were really designed to go under the rear Axle tube of RWD cars where they would allow the car to safely pivot, when you have to start using them sideways with blocks of wood etc on suspension mounting points etc their fine if nothing is moved but generally you then go to the other side of the car and lift that with the jack, thats when they are dodgy.
First rule of safety is don't work under a car supported just by a jack but I have found the quickest and safest way is 2 proper trolly jacks one each side (there is normally only about one substantial suspension point each side for a stand or a jack anyway) either jack can articulate as you pump up each side and even if one fails the car would not fall far also a mentioned the sensible mechanic always puts the wheels under the Sills.
Your right to ask this question as I've seen cars fall of stands more times than jacks and generally when they are still being jacked the other end and no second person is watching the stands.
If you only have a little hobby jack you may be better getting some wheel ramps if it's only oil changes etc