In an industrial setting, process documentation is typically the responsibility of the engineering group. Be aware that when a person goes to school to become an engineer they usually don’t see themselves writing process procedures. In fact, is it probably the least desirable of the tasks assigned to an engineer.
In addition, most engineers are not trained in how to write effective process documents. Considering an organization’s engineers are among the highest paid of the technical staff it makes sense to assign process documentation to a technical writer. Then, the role of the engineer is reduced to reviewing the document before it is finalized. This frees up the engineering staff to focus on research and development and the improvement of existing products.
Organizations which have a just a few or very stable processes may want to outsource process document development. Permanent staff could be reduced to a minimum if they are just required to keep process documents current.