Closing is a verification, not a tidy-up. Resolved means the person who did the work says it is done; closed means quality has checked that it is. Keeping those two separate is the whole point of the status chain, and it is the first thing an auditor tests.
Resolving needs resolve_nc; closing needs close_nc. Reopening a closed NC needs reopen_nc and is always recorded.
Moving the status
Status changes happen in one dialog, and each one takes a comment. The chain is New, Triaged, In progress, Resolved, Closed - it does not skip.

Check that every treatment on the NC is completed.
Set the status to Resolved and say what fixed it.
Have quality verify the fix - not the person who did the work.
Set the status to Closed.
If it comes back, reopen rather than raising a second NC.
Closing is refused while any treatment is unfinished. That is deliberate: a closed NC with open work is the failure mode this check exists to prevent.
Reading the numbers
The dashboard is how the module reports itself: how many are open, how long they take, and where they come from. Average time to resolve counts from the report, so it rewards fast triage as much as fast repair.

By classification type shows what keeps going wrong.
By department shows where.
The monthly trend is the one management review asks for.
Related: record a treatment and triage.