Here are my observations: Beginning with 03, it is printed with a1961, and follows with 04 being b1961. This goes on through 08 being f1961. The next number, 09, starts over with a1961 and proceeds as expected through 14 being f1961. It then appears that what should be 15 would be printed with a1961, however 15 is missing. It then proceeds as expected through 20 which is f1961. It seems as though they are printing either 6 down or 6 across at a time so that every 7th bill is printed with the same plate. However 21 is printed with a1944 and proceeds through 26 with f1944 (once again 6 at a time). It seems they changed plates. Then 27 (which you expect to get printed once again with a1961) is missing. That's the 2nd straight time the bill coming out of a1961 is gone. 28-32 is printed with b-f1961. Have they changed plates back to 1961 again? Then, all hell breaks loose as they begin printing 5 at a time (vs 6 at a time til this point) as they now use a-e1941 and then a-e1967. To finish it off, bills 44 and 45 are missing. It seems 45 should have been printed with a1918 however it's difficult for me to imagine what plate would have printed 44 as they don't seem to be using f1967. Unless of course they are back to 6 at a time and I can't see f1967. EDIT: I JUST NOTICED THAT 02 WAS PRINTED WITH F1967, SO, 44 WOULD HAVE BEEN PRINTED WITH F1967 If they were using plates both across and down, you would have expected the same plate to have printed every 24th, 30th, 36th bill? Unless they cut the sheets and let them blow around awhile.
Okay, I'll give it a go.... Every sequence of six notes from positions A-B-C-D-E-F is coming from a single sheet--the numbering runs consecutively down the sheet. So those six notes will always have the same plate number. And all the serial numbers that land in position F are multiples of 6--that's true all the way through the block. Then the next note after F is the A position of the next sheet. It might or might not have the same plate number as the last bunch, depending on whether or not the new sheet was printed from the same plate as the old sheet. As I mentioned a few posts ago, the BEP's presses use several plates in rotation. So in general, each sheet will have different plate numbers than the previous sheet, with the numbers repeating every few sheets (i.e., every few groups of six notes). I'm not sure exactly how many plates were used on each press in the '30s, but Jamie might know this.... Of course, sometimes a defective sheet was pulled out of the rotation before the serial numbers were printed. And it's also possible that some sheets got rearranged during the inspection process. That's probably why you occasionally see the same plate number appearing for two sheets in a row, and no simple pattern to what the plate numbers are doing the rest of the time.
Knowing a thing or two about early print runs, I can add some comments to these posts: First, bricks did not leave the BEP missing notes in sequence that were not replaced with a star note. The BEP was liable to the Treasury to deliver the exact amount that was ordered, and security was tight, down to the last note, much the same as it is today. Everything was accounted for, whether serialed or not. So in my opinion -- and one which seems to be the consensus -- the OP's missing notes were pulled post-BEP from the sequential runs of notes. They may have been stars, or of some other interest to someone. Now, as for the early printing process in the 1930s and '40s, the presses typically held four plates. There could have been less at times, but for large production efforts, such as with silver certificates, there would have been four plates on the press. The OP's plate sequence of $5 1934Cs has no discernible pattern: 1967, 1961, 1961, 1961, 1944, 1961, 1941, 1967, 1918; and there are 5 plates. But, as 'numbers' pointed out, much less sheets were printed back then -- perhaps a few hundred to a few thousand per day per press -- and they were hand inspected. Then they were layed out to dry on large racks before being sent to the serialing presses. All this individual inspection means that when defective sheets were found they could have been replaced one by one in many instances. Sure, there were times when entire stock of sheets were discarded, but because printing was still a very manual process, it was in the BEP's interest to use as much as it could. So, what may have happened in the above situation is this: The $5 SC Q058...A serials were printed sometime in the second half of 1949. Series of 1934C plates 1941, 1944, 1961, and 1967 were sent to the press on the same day, July 8, 1949, and would have shared the same press. Plate 1918 was already in the pressroom at that time, probably on another press. In the OP's run there is a sequence of the four July 8 plates: 1967, 1961, 1961, 1961, **1944, 1961, 1941, 1967**, 1918; but since the sample set is too small, we cannot deduce the rest. The first part of the sequence, with plates **1967, 1961, 1961, 1961**, is missing 1941, 1944, and 1967, and perhaps these sheets were removed and discarded for some reason, and never replaced with other sheets. They did not need to be if the sheets were not serialed. It is my understanding that groups of sheets were prepared for serial numbering after they were faced and dried. The press operators simply needed 1,000 sheets, and did not care where they came from, or what order the plates (sheets) were in the stack. The lone 1918 sheet could have replaced one of the other sheets, or one of the plates -- we can not know based on the limited data we have. Again, caution must be used deducing answers from such little data to avoid speculation, but the sequence of plates in the Q-A run is probably just the the result of the way the operator created that stack on that day. The order of printing in that era was the combination of many smaller orders: how the plates were chosen from the plate vault; how the plates were placed on the presses; how the backs were printed; how the faces were printed; and how the sheets were organized prior to facing and serialing. And, although the order probably changed little from start to finish, it got mixed around enough to be noticeable. The BEP is nothing more than a production plant. Their only objective is to print notes as fast as they can to fill the orders they need to. Quality control is necessary, but an operational nuisance. If things were out of compliance, they did whatever they needed to do to stay on track -- even stacking sheets in an order not indicative of the order the plates were on the press. If they were in the middle of printing serials, they could have replaced bad sheets on the spot, or discarded them and added a few on the end to make up the difference.