If you were late under your own accord, as in you arrived at the gate anywhere between 30-45 mins prior to your connection's departure, they will probably charge you the same day confirmed fee ($50 or $75 a person). But if your aircraft held out, or you were delayed arriving into DTW for whatever reason they will put you on the next flight if there are seats, if not you get placed on the B1 list as a standby. But if it was a truely missed connection, there is no charge.

zz