Nielsen just claims that if you test with 15 users, you can be pretty sure you have found all problems you will ever find - you most likely won't find any new problems by using an additional 15 or 50 tests. (But obviously you cannot be 100% sure.)
But whether his numbers are based on sound research I wont judge.
Have you ever seen the infomercial for "Dual Action Cleanse" with Klee Irwin? Irwin and Nielsen use very similar methods. The make claims that pass the common sense test, then they use something resembling science to "prove" that they are spouting fact. They are both trying to sell you something, Nielsen has just found a much more profitable customer.
I imagine selling super-laxatives to homebodies and the sleep deprived isn't anywhere as lucrative to selling consulting services to businessmen.
The problem with Nielsen is his "research" is dangerous to the field of HCI and usability. Anybody that uses his "findings" to support their own research is building a house on a broken foundation.
For his business clients this "academic navel gazing" doesn't matter, they probably see the results they were looking for (since he already told them exactly what to look for). Irwin's customers probably get the results they were after too, and whether or not the FDA monitors the claims made by "herbal supplements" probably doesn't bother them much either.
The claim of this article that you can somehow quantify the percentage of usability problems is rather absurd. How can you quantify the total number of usability issues in a program a priori?
Also, I don't think that graph ever reaches 100%, I think it approaches 100% (but then I'm not a math-whiz, so I will gladly accept correction).
They've successfully performed statistical sleight of hand. The assumption that you can quantify the total number of defects is untenable, but they leave that part out of their article and just show the nice charts and math to provide strength to their broken hypothesis.
I think this is unfortunate because I think that there is probably some great insights in this article and the intent is good.
Usability and Human-Centered Computing/Human-Computer Interaction has a tendency to suffer from this type of "pseudo-science" of using fuzzy statistics to present great sounding finding. I was made aware of this trend by the following article:
Wayne D. Gray and Marilyn C. Salzman, "Damaged merchandise? A review of experiments that compare usability evaluation methods", Human-Computer Interaction, vol. 13, pp. 203-261, 1998.