to check a design, you can run MC and corners (like on Vdd, T, RL, CL, fclk, etc.), but doing a MC at each corner combination is far too time-consuming. To simplify the verification or doing an optimization (by hand or automated) it would be much better to know (or 1st to find) the worst-case for each performance within the allowed range of parameters.
But how to find the over-all WC?
Doing 1st a corner analysis is not working well, because some effects only show up once you include mismatch. However, is just doing MC at nominal and then doing a WC corner finding already the full solution? Or would we still miss some WC combinations of statistical and deterministic parameters?
A simple example where "Corners 1st, then MC" fails would be a balanced Op-Amp. Here Voffset over ALL corners is zero due to symmetry, so you cannot find a WC corners set all all. So MC 1st is obviously the better solution. But is this all, end of story?