One theory is that the adjectives become increasingly intrinsic as they approach the noun. Take a "smooth old wooden mixing spoon" for example:
Physical quality (e.g. rough, smooth) may be considered more extrinsic because our experience with physical objects is that they can change. Something created smooth can be made rough if it is mishandled (or something rought can be smoothed by erosion from wind or water).
Age is in the middle, as it can change the appearance of things, but generally in a predictable manner (if at all); an observer may gain other useful information about the state of an object based on its age.
As for material, while there are indeed some physical and chemical processes that might change something known by one name into another (e.g. "tree bark resin" into "amber"), most people would probably agree that a wooden spoon was not once made of metal, nor will it transform into metal in the future.
Function is typically the most intrinsic.
By this reasoning, one would say "smooth old wooden mixing spoon" instead of alternatives such as "old mixing wooden spoon."
In the case of "interactive web-based analytic application," I think this adjective order is suitable. Regardless of whether the application is interactive or web-based, its function is analytic. Function being "most intrinsic," it occupies the spot closest to the noun.
It is debatable whether "interactive" or "web-based" is more intrinsic, but in my mind, "web-based" functions like a material/method of manufacture, as it suggests specific technologies involved in its creation and operation. For this reason, it takes the middle position.
That leaves "interactive" to take the first spot, farthest from the noun. I don't think "web-based interactive analytic application" sounds wrong, just slightly less natural due to the web-based-as-material reasoning in the previous paragraph. It could be argued that "interactive" is actually more intrinsic, because you could implement the same interactive analytic application using any number of technologies, the specifics of the implementation being less relevant to the general operation of the application.
That uncertainty is okay, because these should not be treated as hard-and-fast rules. In an article titled "The Secret Rules of Adjective Order" (2014), John T Beavers, a professor of linguistics at the University of Texas at Austin says:
“The exceptions are so many that it is really hard to arrive at a universal law,” Beavers admits. While “these generalizations capture something important about language, some motivation for organizing it that way,” he continues, “the rules are begging to be broken.”
