You've accepted the responsibility for the work produced by the shop, but it's a shared responsibility. You and your people are a team and the product shipped out the door is the result of the team effort.
It's time for a sit down for a little heart to heart discussion about what is right and what is wrong with the work being produced by the team. It's not time for finger pointing, that rarely produces positive results. What can be discussed by the team is what steps can be taken to ensure it doesn't happen again. Your team will respond if they are as skilled and competent as you say they are. Very few welders or tradesmen want to be associated with poor work or welds.
You can't become a policeman that checks every fit-up, every weld bead, every dimension, but you can institute a system were the welders check each other's work at key points in production.
You can make sure the equipment is maintained and the shop is kept clean and orderly.
You can make sure there are welding procedures to follow to ensure consistency in how the welding is performed.
You can consider using outside resources to assess how the work is being performed and to provide some unbiased opinions on how to improve the shop and the workmanship.
Good luck - Al