Correction...
You were too conservative with the number of sucessful yeilds, and too optimistic with the lead time from finished netlist to production. But, even with a leadtime of half what you've stated, it will be easily made up for in the vastly higher yeilds [6?!?] and the subsequent rapid normalization of yeilds.
So, corrected estimates...
70,000 mm^2 ? Well first the wafer is circular so with quad or rectangle shaped chips we will will not use 100% of the wafer area...
For the sake of the argument let's say they can manage to use only 50,000 mm^2
( 71% efficiency )
Let's take the size of the EE/GS in 250 nm as those were quite big chips... let's add something and assume that each Broadband Engine ( same size for the Visualizer as the Pixel Engine+Image Cache+CRTC take the space of four APUs... ) takes like 300-350 mm^2 ( very big )...
50,000 mm^2 / 300-350 mm^2/chip = 166-142
This means that we would have 83-71 Broadband Engines and 83-71 Visualizers...
Of course I do not expect all the Broadband Engines to hit 4 GHz and all Visualizers to hit 1-2 GHz and work...
Let's go back and think about 12 Broadband Engines and 12 Visualizer fully working per wafer...
That would be 16.9% of the chips produced ( using the 350 mm^2 ).
We are also assuming a launch window from March 2005 to September 2005 ( ~5 months ) and now we are adding the fact that we expect ( low estimate ) only 16.9% of the manufacture chips to be validated for actual PlayStation 3 speeds...
Still, we are getting 12 PlayStation 3s per wafer ( assuming the other components will not be as hard to manufacture... ) and we have 25,000 wafers a month... ok let's assume that we have problems and we get only 15,000 wafers a month... ( 60% )
15,000 * 5-6 ( months before PlayStation 3's Japanese launch [estimated] from beginning of manufacturing including few months for debugging [edit: increased lead time] ) = 75,000-90,000 wafers...
75,000-90,000 * 12 = 900,000-1,080,000 PlayStation 3s
Let's say 600,000 units for the Japanese launch and and additional 40,000 units for post-launch impulse buys: that would give us 260,000-440,000 units for the American launch...
Then you have ~3 months to manufacture more units for also the North American Launch.
Let's keep the manufacturing numbers we have used before...
15,000 * 3 = 45,000 wafers
45,000 * 12 = 540,000 PlayStation 3s
To reach a 800,000 number for the North American launch we would need 260,000 units and we can take them from what was produced before this 3 months period as we calulated above.
I used conservative numbers here also to take into account potential debuging problems with the silicon, delays in the manufacturing lines, etc...
I tried not to be too generous...
And still the numbers do work... that scenario would give quite a good amount of consoles to each region and by January 2006 I expect Nagasaki's new fab to start producing PlayStation 3 chips at a good pace and the overall number of PlayStation 3s produced per month to increase dramatically...
Again this does not include a faster increase of yelds ( expected ) and it is using low estimates for things such as wafer per month output ( 15,000 instead of the estimated 25,000 ) and chip yelds ( 12 chips per wafer validated for full PlayStation 3 speeds and a Broadband Engine die of 350 mm^2 at 65 nm.. they are gettign ready for 45 nm, transitioning as soon as it is possible and this could be an indication that the chip is indeed big... )
