As I stated in the original post we have limited data (i.e. the companion) but we do know the year for 165 AS who attained the shawl so nearly 20% of all Aes Sedai ... admittedly there could be many many more women in any given year, but Moiraine in New Spring also notes the remarkable pace at which the Tower was raising women when she was raised. I find that what's available in the companion is surprisingly in-line with what RJ put in the text. Especially when you consider that the Tower had not housed more than a few dozen Novices at any given time for several hundred years it seems plausible that only a few women in any given year would attain the shawl.

From the data available to us there is an obvious trend of quickly being raised to the Shawl around the time of the Vileness.