Update: I recently made some changes to this article. Most assumed that I was in favor of always slowing down to increase throughput, but it’s actually only advisable if you can increase efficiency by a significant amount (10-20%). All the changes are in the last paragraph.
Can you increase efficiency and throughput by slowing down?
I recently had a discussion with a customer and an engineering firm about increasing throughput by slowing down the rate of a labeler from 400/minute to 380/minute. They recorded an improvement in efficiency to justify the change. I questioned the decision from a thruput standpoint and wanted to come up with a good way to determine if an increase in efficiency actually increased the thruput or not.

Is slower better?
Efficiency is calculated using the following formula:
MTBF / (MTBF + MTR)
MTR = Mean Time to Repair
MTBF = Mean Time Between Failure
A properly buffered line should have capacity to handle the longest MTR on the line. The difference in maximum rates should be such that the table can go from full to empty in less time than the MTBF. For example, if you have a line like this:
| Name |
Max Rate |
MTR |
MTBF |
| Filler |
330 bpm |
3 min |
60 min |
| Buffer |
990 bottle capacity |
| Labeler |
400 bpm |
? min |
? min |
Your labeler must have a MTR of 3 minutes or less and an MTBF of 9.9 minutes or more, giving us a minimum labeler efficiency of 77%. So what if I decrease my max rate in an effort to improve efficiency?
| Name |
Max Rate |
MTR |
MTBF |
| Filler |
330 bpm |
3 min |
60 min |
| Buffer |
990 bottle capacity |
| Labeler |
380 bpm |
? min |
? min |
My minimum required MTR is the same since I’m still filling the buffer at 330 bpm, but my minimum required MTBF is now 19.8 minutes. This gives us a way to measure whether the decrease in rate has affected throughput. My labeler efficiency must now remain above 87% (19.8 / (3+19.8)) to keep the filler running and maintain throughput.

As the labeler slows down, its efficiency must go up to maintain throughput for the packaging line.
The formula can even more simply be expressed like this:
e = (Fr / Lr)
Where e = the minimum efficiency needed to maintain throughput
Fr = the max rate of the constraint
Lr = the max rate of the machine in question
If I run the labeler at 400 bpm I need to maintain a labeler efficiency of 77%. If I run it at 380bpm, I must maintain an efficiency of 87%. So if slowing the max rate of the labeler resulted in improving the efficiency from under 77% to something over 87%, then yes it will have improved throughput. If they were already running above 77% prior to the rate change, then throughput will be unchanged. If efficiency is under 87% after the rate change, then throughput will decrease.
In practice you have to find the right balance between rate and efficiency. It may be tremendously more difficult to maintain 87% than 77%, due to inconsistent materials or operator error.