Depending on the artery, the person cut loses blood pressure; some arteries quicker than others.
For an example of the importance of blood pressure, consider how woozy a person can sometimes feel just from standing up too quickly.
James Sass has a table on one of his web sites that gives time to unconsciousness according to the artery cut.
For a silent kill (just conversationally speaking), an artery will not do the job.
Even with a neck artery, my 1960's Marine Corps instructors told us to expect a lot of noise, if only from the blood going down the airpipe and the air coming up, and a few seconds of noisy struggling.
My instructors strongly recommended the kidney because a person stabbed in the kidney instantly goes into a state resembling shock.
Anyone who has passed a kidney stone can attest to this.
Most people who have a kidney stone fall to the floor and lay there quietly, unable to do much more than roll over, if that.
Additionally, most of us have an intuitive understanding of the location of the kidneys.
In a real fight, many people will strike the kidney area of their opponent without really knowing why they do it.
In the summer of 1967 I rendered an "opponent" unconscious with one blow to his left kidney.
He went down like a sack of bricks and lay there without moving or making a sound.
A blow with a heavy object to the nape of the neck (the bump above the shoulders) and/or a stab to the kidney with a proper knife (FS dagger or Gerber Mk II} provide the highest probablility of a relatively silent, instantaneous disablement.
If one doubts his ability to visualize the kidney in another human being, he can pick up a big rock (an M-14 rifle butt, tomahawk or heavy stick will do) and aim for the base of the neck.
Even then, no guarantees.
As an alternative, consider bribery or stealth (sneaking around).
Aesthetically and morally much more pleasant.