My definition of a Failed Change is one that generates unexpected (or unforeseen) Incidents. The Impact of the Incident may need to be High for me to consider the Change a Failed Change (or some other scale of Incident Priority), but remember that the goal of Change Management is in part to “Minimize the impact of Change related Incidents”. If an implemented Change fails to meet the goal of the process, then I would consider it to be a Failed Change.

I would put Changes that had to execute the approved Back Out Plan in a different category than Failed Changes.

I would also say that is important to keep metrics on both categories.