If the sticks of RAM are not from the same brand or have different capacities, they may have different bus speeds and voltage requirements. For example, I originally had (2) 1GB sticks of Corsair Dominator RAM in my machine. These sticks required 1.8v . When I added (2) 2GB sticks of Corsair Dominator RAM (giving me a total of 6GB system RAM), that was when I ran into problems.
Even though the bus speeds were the same, and they were from the same product line, these bigger sticks required more voltage. The 2GB sticks required 2.1v; the 1GB sticks required 1.8v. My motherboard isn't designed to deal with varying voltages in its RAM slots. Because the first required 1.8v and the 2nd pair required 2.1v, that was the cause of my BSoD. Solution? I removed the smaller capacity sticks and just stuck with the bigger ones. Eventually, I will buy 2 more sticks that are identical to the 2 currently on the board so that my board will be maxed out (to 8GB).
Before investing in different capacities of RAM, I would do the research on your motherboard to ensure that it can handle differentiating voltages within its RAM slots simultaneously. Also, I noticed motherboards have a tendency of underclocking RAM due to the improper amount of voltages. Be sure you can tweak the bus speed and voltage to the RAM to ensure proper performance. BSoD typically occurs from the RAM if the RAM is damaged due to improper amounts of voltage, so be careful when tweaking the voltage! When purchasing new RAM, be certain to always do a memory diagnostic to make sure it didn't get damaged from static electricity during storage from the manufacturer.