This year NVIDIA fell victim to its own set of GPU failures resulting in a smaller-scale replacement strategy than what Microsoft had to implement with the Xbox 360. The NVIDIA GPU problem was well documented by Charlie over at The Inquirer, but in short the issue here was the solder bumps between the GPU die and the GPU package substrate.
Traditionally GPUs had used high-lead bumps between the GPU die and the chip package, these bumps can carry a lot of current but are quite rigid, and rigid materials tend to break in a high stress environment. Unlike the bumps between the GPU package and a motherboard (or video card PCB), the solder bumps between a GPU die and the GPU package are connecting two different materials, each with its own rate of thermal expansion. The GPU die itself gets hotter much quicker than the GPU package, which puts additional stress on the bumps themselves.
In 2005, ATI switched from high-lead bumps (90% lead, 10% tin) to eutectic bumps (37% lead, 63% tin). These eutectic bumps can't carry as much current as high-lead bumps, they have a lower melting point but most importantly, they are not as rigid as high-lead bumps. So in those high stress situations caused by many power cycles, they don't crack, and thus you don't get the same GPU failure rates in notebooks as you do with NVIDIA hardware.
What does all of this have to do with the Xbox 360 and its red ring of death problems? Although ATI made the switch to eutectic bumps with its GPUs in 2005, Microsoft was in charge of manufacturing the Xenos GPU and it was still built with high-lead bumps, just like the failed NVIDIA GPUs. Granted NVIDIA's GPUs back in 2005 and 2006 didn't have these problems, but the Microsoft Xenos design was a bit ahead of its time. It is possible, although difficult to prove given the lack of publicly available documentation, that a similar problem to what plagued NVIDIA's GPUs also plagued the Xbox 360's GPU.
Page two of the article shows you how to find a Jasper. If you look at the barcode on the back of the XBox 360, and it says "12v-12.1A" then it's a Jasper. Earlier versions have 12V @ 14.2A or 16.5A. Also, if you can look at the bottom of the power supply brick, it will say "150W" for a Jasper. (Jasper PSUs have a slightly different connector than older model 360 PSUs.)
But will Jasper fix RRoD? Only time will tell...