The popular methods seem to involve test scores and graduation rate. Test scores are a valid part, but only a part: education is not test prep. Graduation rate shouldn’t be a factor at all, since it isn’t independent of school policies.
A natural approach would be to identify the measurable effects of education. Then, identify the non-school factors influencing those outcomes. Then, predict outcomes based on those factors. Achievement beyond the prediction is probably due to the schools. For example….
Measurable outcomes of schooling probably include SAT scores, college attendance, college success, employment, and crime rate. These are aspects of a post-schooling life influenced by education.
Non-school influences on those outcomes probably include the average (and median) income and educational level of neighborhood families.
So, a given level of income and education in a school’s families should predict a certain level of outcomes (SAT scores, crime rate, etc.) in the school’s students after they finish school. If the school does better than what is predicted, it is a successful school.
Generally, statsitics are relevant to groups. This method wouldn’t work at all in assessing individual teachers. It might be better at assessing districts than schools. All such methods are aproximate. Something is always lost in a statistical snapshot.