Model Advice - Time varying success rates of hospital data with small dataset

Hi Pymc3 community. I am pretty new to this community so any help or advice is greatly appreciated.
I am trying to build a model evaluating the success rates of a hospital procedure over time and predicting a success rate in the future. I think a Bayesian approach fits this type of problem. The data is reported as a yearly success rate for each hospital, meaning each hospital only has a few data points (~10). There are some other features in the data that may be useful, like number of procedures, but nothing strongly correlated to success rates.
I was thinking of modeling this as a hierarchical problem since I am trying to separate the natural success rate distribution from the hospital efficacy. However, I am no longer sure this is the best approach since my simple model ends using a normal distribution for the mu and sigma produces the same success rate for every hospital.
I would really appreciate any help working through this problem! Thank you!