Agreed that EWMA could be used, but it has it's complexity.
The different weights of a time series is used in forecasting to give more importance to some values (specially to the last) so the trend of the data is affected more from the last values.
For example if I am forecasting sales and I take the last 10 years to do the job, I can't give the same weight to the values 10 years ago and to the values of the last year/month, because the grow of the market, new tecnologies and many other factors.
WMA is one of the forecasting methods (the simplest ones, and technically is just smothing) but you can use EWMA, Winters or many other.
As I said, it is an uncommon aproach, but if Sanjoh has an SPC/Statictics program with EWMA, it could be a good idea to give a try, but I recomended WMA because it's easy to try in EXCEL and see if could give him what he was looking for.
Other way to do the job, Sanjoh said to Geoff about the direct use of 1,2,3 coding "That works ok for general trends. It leads to lots of false positives when using xbarnr due to the low measurement resolution.", is to change the rules of detection acording to his process. One important thing about rules is that not always apply (for example in chemical process were a measurement has too much to do with the last measurement).
By the way, you said "Would a simple bar graph, with 3 bars (1 bar for each category) for each lot (each lot being noted on the X-axis) show what you are looking for?"
Just a question, how a bar chart can give, as Sanjoh said "detect shifts in the process"?