There are a couple of comments I'd like to add.
First, on the issue of no theoretical VisVSA background material - keep in mind the following. VSA was a company purchased by Engineering Animation Inc. prior to EAI being purchased by UGS. VSA was primarily a consulting company that wrote software for the use of its consultants. VSA was never serious about the sale of software per se. As such, not only was there never any motive to document its software, anything that imparted knowledge to the users took consulting business away, so it was in VSA's best interests for this to remain a "mystery". It is Monte Carlo simulation based, which is about all anyone knows about it. Its subsequent owners had an appreciation for GD&T about equal to the average engineer, so its no surprise that information about it is limited.
Second, on the issue of the vector loop vs. Monte Carlo simulation. Vector loop methods are in general very fast, and the do not require actual shop floor results data to be effective. The tradeoff for this is that vector loop performance deteriorates rapidly as the size of the problem increases, and it does not take into account variability that is introduced as a result of variations due to manufactuing methods and machines. In all cases, IMHO a Monte-Carlo based simulation approach yields superior results, and can do so on very large problems (i.e a complicated assembly with corresponding tooling), but to be most effective requires results from shop floor operations to model the variation upon which Monte Carlo simulation depends.