Classification name needed

I would probably count it as time compared to the due date.  Therefore, negative days would be “earlies”, 0 days would be “on-times” and positives would be “lates”.  I would look for what kinds of factors were more likely to create earlies, on-times and lates.
Your spec limits would proably be some range of maybe a day or two early or a day or two late–depending on your process.  The shape of your data will tell you a lot about your process–that is, are people actually working towards the target or is it a pure normal distribution.
Best Regards,
Gordon

Incidentally, GE changed the definition of span to be the 1st and 99th percentiles as they got better in meeting customer want.  The idea was that if you use 9/95 span, you are essentially still dissatisfying 10% of your customers (or 10% of your deliveries).  The 1/99 Span tightened up the requirement so only 2% of deliveries were excluded.  Obviously, you still worked to reduce those as well, because they are certainly defects to the customer.
Another concept that comes in here is that “earlies drive lates”, that is: when the process is delivering a lot of products early, (which is not always a good thing), it is often causing something else to be late.  As you look at your process, keep your eyes open for cases of what may be causing some items to be early at the expense of others.  If this is a people-driven process, you may find people doing their own form of arbitrage, completing the easier/more reqerding/more ‘urgent’/other items first.
Best Regards,
Gordon