I joined the company at the beg. of January as a manager to take over a team. It has been very intensive from day 1. We had deliverables even on my third day. It's my first management position.
There's a person in my team who is very friendly, well-liked and smart but also totally chaotic and unreliable. Her results have been poor and I end up doing her projects for us to meet deadlines. She's well-liked and enthusiastic but our job requires attention to detail and being at least to some extent structured, which she doesn't seem to have.
It's nothing personal. I like her as a person, think she has a great personality, it's just that her work is a source of problems for me.
I mentioned to her in our 1:1 - in general terms - how important it is to work accurately, even if it costs time. I told her that rushing through is not expected in the team and that I definitely prefer people signaling problems and us thinking together what the solution could be instead of delivering substandard solutions. I told her we are all humans and make mistakes, which is ok as long as it doesn't happen much and that we (all team members) should try to reduce the number of mistakes.
It didn't bring anything. Her work quality is still really bad.
At the same time... I'm new. Everybody, including my bosses, likes her here. I'm not sure how to deal with bad work as a new manager. Should I keep my mouth shut? Should I mention that to my boss?