I work for a small engineering and manufacturing company. To date our production process for each product has been defined in each critical aspect by the design engineer, then handed to the production department and rarely looked at again by engineering. Many noncritical aspects are undefined and left to the variable judgement of the assembly workers. I'm considering assigning an engineer to the task of analyzing and documenting the entire production chain of a product for consistency and quality purposes, and to look for cost saving improvements. What discipline of engineering would this be considered, if any?
Most engineering discipline are capable of defining manufacturing and test process. It is the management function to ensure the processes are followed. Generally depending on the size and structure of the organization most defining manufacturing and testing process are mostly handled by manufacturing test and process engineering teams. If a Quality organization exists this team gets heavily involved in ensuring the implementation and monitoring of processes.
In the event of the quality related issue the quality organization gets involved in root cause and analysis of the quality related issue. In event of issues with the manufacturing process the changes are made the to process through the use of a change management process.
Also periodic quality audit are established to ensure if the manufacturing and and test process are followed per the definition. This is an proactive measure.
This question and response is loosely tied to one of your previous questions How can I arrange my ECO system to enforce the principle of least privilege?
There are statically process control, six sigma - continuous improvement that can address some of the above mentioned issues.
A Quality Engineer with direction from management as well as significant support from manufacturing and design engineering can address the this issue.