There's no formula for how to proceed, but we can offer some guidelines.
Start by being as clear as possible about where you and your group want to go. Make sure everyone is part of that decision and is committed to it. Otherwise, any actions you eventually take will appear arbitrary and even unfair.
Given the goals you've set, work with your team to identify their roles in making the change. Discuss with the group about how you may need to change as well. Make sure you're not the one who's good but not good enough.
Give everyone the opportunity to rise to the challenge. Give them the training, coaching, time, attention, and, most of all, the feedback they need to improve.
If and when you begin to sense that someone may not make it, keep working with that person, but it's also a good idea to start to talk to your company's HR department about the issue. There are policies and practices that you will likely need to follow.
Make sure the person in question knows where she stands by giving them regular feedback. She deserves to know not only where she stands but also what's at stake.
Once you decide someone won't make it, try to find another position that will work for that person, either in your group or elsewhere in the organization. Consider re-assigning roles and responsibilities to recognize her strengths, weaknesses, and potential. But don't compromise on what you need.
Above all: throughout this difficult process, it only pays to treat people with dignity and respect. It doesn't help matters if you try to make yourself feel better by demonizing someone -- that is, by finding fault with everything that person does to justify what you must do.
Be aware that, no matter what you do, your final decision -- to keep this person on or fire them -- will always be a judgment call to some degree. Could the Beatles have become stars with Pete Best instead of Ringo Starr? Who knows?
Many managers duck the whole difficult issue by making no decision at all or by putting it off forever. However, if you and your group aspire to be more than you currently are, it's a call you will have to make. It's one of the most difficult choices you will face, one that will keep you awake at night, but you cannot avoid it.
Linda A. Hill, a professor at Harvard Business School, and Kent Lineback, a writer with 30 years of management experience, are co-authors of Being the Boss: The 3 Imperatives for Becoming a Great Leader.