Ok, a lot of people work on semantics. Whether it's on time "delivery," "shipment," or whatever you want to call it is meaningless. In fact, for most shops like us (component contractors) legal "delivery" is at the shipping dock. Stay away from semantics. So you set a date to ship in your system and the question is whether you met that shipment date or not.
If you didn't meet that shipment date, then why not. That's where we do our pareto chart. We monitor things like capacity, incoming metal delivery, delays at plating/painting vendors, machine problems, tooling repairs, etc. Now our method of tracking these issues is really complex -- our production manager writes it down on his weekly shipment reports and we sit down and compile all the info monthly.

Like any job shop, our biggest issue is capacity. So we look at that for ways to improve.
As for your part specific questions, do you have any ERP management system at all? Or just trying Excel and word? Have you done a map of your process to take an order thru production? Do you have any idea where the time sucks are? How do you get an order from PO to shipment? Good luck.