"a strict supervision" is a correct and usable phrase in written English.
It generally is used to refer to a close monitoring or evaluation of something. For example, "The school has put in place a strict supervision of students leaving the campus during school hours."
In September 2010, after years of debate, the Food and Drug Administration severely restricted Avandia's availability, allowing it to be prescribed only to patients in a special program who had not responded to other drugs and were taking the medicine under a doctor's strict supervision.
In one of that vast township's more remote districts – named Jabulani, the isiZulu word for "joy" appropriated by the manufacturers of the 2010 tournament's official ball – we found a group of small boys who call themselves Jabulani Arsenal, practising under the strict supervision of a teenage girl with a referee's whistle.
Kosher Kosher turkeys have been slaughtered in a humane-as-possible manner under the strict supervision of a rabbi.
North Korea has sentenced the children of two defectors to hard labour under strict supervision in a case that paints a picture of the harsh treatment meted out to the relatives of those who flee the regime.
He got locked up in 2000 for everything from weed to carrying a gun on parole, and only got out a few months ago under strict supervision.
Patients were mobilised in the initial 48 hours under strict supervision either by a physiotherapist or a nurse.
The six counter that the Nuclear Non-Proliferation Treaty has no explicit "right to enrich," only the right to a civilian nuclear program under strict supervision by the International Atomic Energy Agency, and that Iran has been out of compliance.
At this time, most computer "labs" in Indian schools were one or two computers that were only to be used under the strict supervision of a teacher.
The pre-test and post-test were taken over the web during school hours, under the strict supervision of a teacher.
