In my opinion, the NCR should be filled out by the organization's QA/QC Manager or his representative that received the NCR.
It should then be reviewed after corrective action has been performed by the NCR originator and if satisfied, closed out.
In my view it can be done in two ways; (a) If the non conformity was noticed by production department during manufacture of the goods before it was offered for inspection checks, head of that production section had to raise an NCR and that NCR had to be countersigned by the respective quality control engineer of that section. After the non conformity was attended by the production department, this had to be once again countersigned by the respective quality control engineer confirming the conformity and finally this NCR had to be closed by the management reprasentative of Quality control department. (b) If the non-conformity was noticed by the quality control engineer during his inspection, the NCR had to be raised by that quality control engineer and it had to be countersigned by the production dapartment head. Once this non coformity was resolved, the same quality control engineer had to countersign the NCR confirming the conformity and it had to be closed by the management reprasentative of Quality control department.
I Think Design department should also be involved there should be also comments and signature from Design Department that whether it is accepted or if it is affecting some change in Design part of view then he will raise a DCR to client and upon client acceptance of that DCR the NCR will be closed.