Who owns FMEA

Mandy,
I’m not sure I understand what you mean by ‘own’.  If you are referring to who would be responsible for updating and keeping current the actual document, that might be the Process Engineer or the Quality Engineer for the process or product.
If you are referring to who might be responsible for communicating any changes to the process that need to be updated on the FMEA document, that would possibly be the process Supervisor or Process Engineer or the Process Improvement Team.
Usually the problem is ensuring that any changes to, or discoveries concerning the process are communicated to all stakeholders and documented on the FMEA.  The FMEA changes should then be discussed or addressed by a cross-functional team to ensure that the changes made are not just one person’s opinion as to the ratings for severity, etc.
If this doesn’t answer your question, please clarify.

Stan, I agree, but I am astounded how many organizations have a difficult time identifying the process owner. Functional owners abound, but process owners is remain rare. Pete

Stan & Pete,
I agree with both of you. The owner is who owns the process. But the more proliferation we see in matrix type organizations makes this more difficult to define.
Therefore, if the FMEA should be owned by anyone, I say the Champion who is responsible for improving the process owns it, regardless of the matrix and actual functional and process owners. Let the Champion deal with the various roles and owners.
Regards,
Dr. Scott