It looks like they're displaying the failure rate in year 1 (of owning the console, apparently).

Guys, you should really dust your math. This is not calculus and hardly algebra, and there's no such thing as "setting an equation to zero" :)
Anyway, by glancing at the report PDF, 16K is the number of consoles over which the rates were calculated (360+PS3+Wii).

I think it is logical to assume the 360 and PS3 will have higher failure rates simply down to heat fatigue alone. The Wii is more like a normal consumer product in that regard.

Proper ventilation is very important with these devices. I suspect the PS3 to have increasing failure rates based on usage and age also the same should apply to the Jasper units although you would expect Microsoft to have learnt more about the heat issues and corrected them longer term but that might not of happened.

The new PS3 Slim sounds like it expells a lot more air directly via an exhaust in a more traditional way. I am not sure how well it will perform in poor ventilation but my experience with the original PS3 is it seemed to cope but for how long is questionable.

REALLY...so can you give us a breakdown of how many of each console was in the group of 16,000?

@ theprof00

Can you tell me  where did you get 70K...was it in the report and i jsut missed it?

23.7% of consoles repaired was 16k right? 23.7% error rate, and 16k consoles were repaired right?
100/23.7=4.24 or something. so, multiply 16k by that and you get the total consoles... unless werekitten is right and 16k is the total number of consoles they cover.

@werekitten
wow....wow....wow....no such thing as setting an equation to 0.... just wow

so whats 5x+12=0? I'll tell you... it's setting an equation to 0. That is algebra, which is based on variables like x,y,z and others.

because there are some unknown variables, like the customers who sent their consoles to MS, you can use a variable to figure it out partially.

Basically there is a 23.7 fail rate on consoles which they've covered AND repaired.
They said it could be as high as 34 or something, so that's an additional 11% or so of the total number.
Then there is also customers who didn't tell ST at all about the failure and sent it to MS automatically.

But like I said before, this problem will actually require statistics to find a distribution range over the 34. Since they haven't said anything about their math, it's especially difficult, because they might have gotten that number from standard distribution already, which would mean that if I made one, it would be completely worthless.

It's not difficult, I just don't feel like doing it. It's tedius

No to some of your assertions.

The total number of consoles reparied were 16000

Out of all the consoles covered by Square Trade the 360 has a 23.7 failure rate, the Wii a 2.7 failure rate, and the PS3 a 10 failure rate.  You can form a relational quation based the 9Xbox + 4 Ps3 + 1 Wii equal the 16000 failures.  That's a 3 unknown variable problem, and if you can solve that without calculus and Diff Eq. more power to you.  Maybe I'm missing something, but I didn't see any other data points.  But we are going down a math rathole...

The key statistical data points are:

- M$ started the 3-yr RROD repair effort in July 2007...and the number of reported RROD cases to Square Trade didn't drop, instead it when up.

- Likely, based on the data, the RROD problems are abating as the newer Jasper chipsets hit the market, and if you remove RROD, 360 has a failure rate on par with PS3...ofcourse that like saying if I was 6' 5", and If I could shoot like Ray Allen, and I could dunk like Vince carter, and play defense like dennise rodman, I'd be in the NBA right now...lol.

@theprof
As for the 35% number, if you read the PDF it's explained how they came up with that, but it's a very gross estimate with no statistic involved, simply based on an email survey among their customers.

PS: I don't want to argue about the "equation" issue, because it's hardly relevant, but you're not expressing yourself correctly from a mathematical standpoint, trust me and/or verify it from other reliable sources.

Sure...send me a PM...Can you give me a simple way to solve it?

The Jasper chip seems to have cured the problem.

like i said before I was interrupted by werekitten, you can use statistics to find a distribution graph.
You use a one direction distribution, starting from the base, 16k consoles (if im correct that that is the number of 360 consoles) and moving upwards, because you can't have less than what exists.

The distribution will come up with 67% followed by 28%, which would equal 95% of the consoles with problems. It would probably be something like 18 or 19k consoles.

You can then use the number of consoles within the distribution to find out how strong that number is. If there are enough consoles in the sample, you can get a pretty accurate reading as to how strong the distribution is.

But then again, that's the only info you have. It won't as accurate as possible, but it's one way to get a more accurate measure.
The idea is, that it's definitely more than 16k, but we don't have those numbers. The distribution is only a way of finding a realistic number, one that would make sense, that's it.

However, there are times when numbers don't make sense. They may have sent ony a couple hundred to MS or a couple thousand or 10 thousand we don't know.

You are right about the calculus. It is possible to solve equations with 3 unknown variables through calc, but it will only be an estimate.