This morning's Technology section has a short piece asking precisely that question - to which Microsoft doesn't have a clear answer.
Basically, how many people are getting the Red Ring of Death? (You know, where the power button just shows red, and sticks there.) There is an alleged cure - but read on: it might have a real, physical cause.
According to figures put out by Microsoft, it's around the industry average of 3-5%, though of course as Microsoft has sold north of 10m consoles, that still works out to anywhere between 300,000 and 500,000 bust ones.
But Tim Anderson suggests that the numbers might be significantly higher, pointing in particular to a survey by Xbox360 Gamer which found some people who'd had up to 7 faulty consoles.
Is that a lot? Are the numbers out of line with Microsoft's claim? This is probably an example of a Weibull distribution (much used, apparently, to model hardware failures). There's a page with some calculators here, but I've got to admit to not having the statistical chops to know what numbers to plug in. Statisticians, awake!
One possible cause though if the failure rate is higher than the industry average could be thermal stress: the Xbox 360 gets very hot (hear those fans!) and that can lead to stresses on the solder of the chips, eventually leading that solder to crack. Precisely that problem lies behind the failure of Apple's iBook G4 - as shown by some fine Danish detective work (a phrase we don't use often enough).
Microsoft did come back with a reply which we weren't able to use enough of in print, so we're glad to reprint more of it here:
We can not provide specific figures, but can confirm there is not a single root cause or systemic issue with any of the Xbox 360 consoles. With such a complex consumer electronic product that contains more than 1700 different components and 500 million transistors, there are obviously many things that can malfunction at any given time. The vast majority of customers who own Xbox 360 consoles continue to have a terrific experience.
Oh, won't anyone think of the transistors?