I have heard from others from 5 yrs to 10yrs. I have even heard 1 yr if the student is incredibly diligent in practice. My own personnal experience tells me between 5 and 10. The problem is, not only are we all different, the arts are different. What may be a brown belt in one art may be a black belt in another.
Some arts have a minimum amount of time required to earn rank.
Some promote depending solely on ones ability and how long he has studied is of no consequense. In retrospect, anything is possible when one is on their way to making rank. Maybe 1yr is o.k., however, whether or not there is validity in the rank may be in question. There is more to martial arts than just moving around learning forms or techniques. Anyone can learn to move around.