I work with a lot of MPE's at my job. We're typically at the tail-end of the building process of any part. It's already been designed, and most of the kinks should already be out (although, often times there are still many to iron out). Assemblers who build the product are expected to make them to a certain quality, and when a part fails or is incorrectly built it is up to us to see where it failed and how to fix it. We write the processes in our computer to tell the assemblers how to fix the problem. It allows more opportunity to get up, walk around, take apart products and get a good look inside to see where the problem lies.
I know a few people who love their job as Manufacturing Process Engineers because they don't like to just stare at a screen all day. It depends on what you like doing the most. I don't mind staring at a computer, but I don't mind looking inside jobs and finding out what makes them tick, either. We do spend a lot of time on the computer writing processes, however. If you like seeing a product, being able to tear it down and figure out how to make them better, you'd like being an MPE.
Note: I work for a company that doesn't have an assembly line. They provide mostly low-volume products that are assembled by hand. The atmosphere for an MPE at Boeing would be drastically different, I imagine.