Again Nicholas, you are right, but I'm not explaining things regarding my POV very well either. It has been years since I had to operate one of these danged machines.
Basically, I've gotten the analogies all mixed up now and no-one will probably believe any explanation, but just like the car assembly example, it takes time for the first finished product to come off the line. In the case of a car it is 12 hours and in the case of the film it is 1 - 2 hours. If you make 120 cars or process 120 rolls of film it will then take 12 hours and 1-2 hours respectively + 2 hours for both. So, for the film at 1' per roll throughput it will take 3 - 4 hours to produce the first 120 rolls of film and after that it will take 1 hour to produce 60 rolls. In a normal shift operation, one shift, by that estimate will produce about 360 rolls of film (one shift, one strand, one machine and 5 hours of output with 3 hours of startup and shutdown). In a week, that is 1800 rolls. Some machines run more than one strand, and there may be more than one machine in case of mechanical breakdown.
Maximum efficiency is achieved in both and assemly line and a processor when they are running constantly, but with film the processor takes some time to warm up before it can be used after a shutdown overnight. IDK about the car assembly line, but it probably can be started "cold" and can be turned on and off. Only the drive for the processor can be started and stopped.
So, your statement: Steady State Throughput = web length in rolls / process time should be modified to include the startup time during which everyone but the splicing technician is idle so to speak. They are doing other related tasks but not finishing slides until the process time has elapsed and the first complete roll emerges. AFAIK, they cannot start work until they have a full roll in-hand.
So, your formula should also be modified to include the fact that the web length in rolls is usually not handled until that roll is finished. It is cut at the leader, and the leader winds until more film appears at the tail of the machine.
So, unlike a car which can be driven away at the end of its production, the film cannot be removed one roll at a time until an entire spliced roll is finished. Now, this is the way it worked when I did it. We had to wait for a full roll. In fact, we usually did not make up the entire 1000 ft roll. We used about 200 ft rolls to cut the cycle time down. That way the chopping and packing operation got started more quickly than if we did 1000 ft rolls.
In fact, we processors did the chopping and packing as well and rotated through our lunch hour leaving one person to attend the machine while these rolls came out of the machine. Then as we returned from lunch we either replaced the watch operator or began chopping and packing individual orders.
I'm sorry for my poor explanations, but I hope I got the intent right in this one. Having done this, but not for years, I know that it is a long process and a long sequence of events.
Apologies. And, thanks Nicholas.
PE