Good advice from Barry. Definitely get that owner identified, as at senior level as possible, and ensure the importance of Problem Managemnt to the organization is communicated widely from senior managers in all departments. This is where the analysis of repeat incidents will be useful, to start to build the case and to set meaningful targets.
Carry out some basic training in methods and techniques to give people confidence and to provide a foundation in consistency of approach. You will likely also find that you need to review your current incident classification and probably tighten up the closure codes and standard format closure comments in order to improve the effectiveness of the analysis process.