You can find your answer in the Rules section under Ship Production.
I believe for you to be able to produce a ship, you need an SY (shipyard) or factory, the appropriate privileges, the credits, and the DC (datacard), the builders, and the RM's (raw materials).
That's all I know. I don't know if that really answers your question.
Factory ownership is irrelevant, ask half the independent producers. You need to have the faction set as manager of the facility, and you need someone within the faction type to start the production run. After that it works fine regardless of what faction you are in.