FMEA is just one of the tools used in Risk Management, similar to Ghantt chart used in project planning; so, I'm not sure if asking how does FMEA interact with CMMI is an appropriate question.
Are you looking at how software risk management or certain risk methodologies interact with CMMI?
I'm not sure how helpful I can be, but I will try. If your company is evaluated to CMMI, it means you have a documented system for your software (from understanding the requirements, to creating your work breakdown structure, to communicating to the shareholders, to training, planning, developing the SW, testing it, validating it, verifying it, etc.)
You would take this process and use it for your FMEA template steps. for example:
1. Process step: Requirements management
2. Potential failure mode: Fail functional test.
3. Potential effect of failure: delay in deliver, customer not happy, etc.
4. Severity: 5
5. Potential cause of failure: missed entering the requirement
6. Occurrence: 3
7. Controls in place (Prevent): None
8. Controls in place (Detect): automated calculator for number of requirements
9. Detection: 5
10. Risk Priority #: =5*3*5=75
11. Action to put into place... etc.. etc.. etc...
Once you have listed all your software process on the FMEA template, the team can go through and perform the exercise. its a good starting point.
I hope this helps.
So, I think FMEA is calling for Project Risk Management (Maturity 3) and for Casual Analysis and Resolution (Maturity 5) in CMMI.
Software FMEA sounds a weird think to me, due to the probabilty that the software will fail is 100% for me.
There could be however some analysis in design phase to guide the selection of alternative approaches, mostly to prefer the kind of design that inherently eliminates those suspected potential problems.