Re: P Charts - Subgroup Size?
I usually find it best if there are at least 20 in each subgroup. This keeps the p chart control limits "reasonable" (doesn't work well if the LCL is less than 0%and UCL is greater than 100%).
Generally speaking I would not try to artificially align the subgroups to changes in the process - I'd let the data speak for itself as to if a shift is found.
Yes, you could do random sampling and then plot that data if it really is too hard to deal with all of the data.
"A Passionate Statistician", ASQ CQE, ASQ Fellow