In my previous post about throughput line analysis, I discussed the case of how to size buffers in a simple, linear, production line. What do you do if you have machines that run in parallel, such as two labelers?

A simple packaging line with multiple paths

Each product can take one of two paths through this packaging line. Throughput varies depending on the rates and efficiencies of each machine like a normal production line, but here you have something different. If one of the labelers is down, production can continue at a slower rate. How do you calculate the throughput of this line?

Note that the line will run normally at 500ppm, unless one labeler is down. Then it runs at 300ppm.

A linear production line has only one running state: The state when all machines are operating. The throughput of a linear line is calculated with the following formula:

Throughput = Machine #1 Efficiency * Machine #2 Efficiency * … Machine #N Efficiency * The Max Rate of the slowest machine

Where N is the total number of machines.

By multiplying each machine’s efficiency together you are calculating the percentage of time that all machines are operational. We can also use this formula to calculate the frequency of a state when one or more machines are non-operational. This simple non-linear line has three running states.

State 1: Filler On, Labeler 1 On, Labeler 2 On, Packer On (This produces at 500 ppm)
State 2: Filler On, Labeler 1 Off, Labeler 2 On, Packer On (This produces at 300ppm)
State 3: Filler On, Labeler 1 On, Labeler 2 Off, Packer On (This produces at 300ppm)

ppm = products per minute

Now we need to calculate how often the line is in each of these states. State 1 is calculated like the linear packaging line. Just multiply each efficiency together:

0.98 * 0.95 * 0.95 * 0.94 = 83.14%

Our line runs in the optimal, 500ppm state 83.14% of the time.

To calculate the percentage of time in the other states, we need to multiply each efficiency together for running machines and (1 – the efficiency) for all non running machines:

0.98 * (1 – 0.95) * 0.95 * 0.94 = 4.38%
0.98 * 0.95 * (1 – 0.95) * 0.94 = 4.38%

So State 1 occurs 83.14% of the time, State 2 occurs 4.38% of the time, and State 3 occurs 4.38% of the time. This is independent of any duration of time, so we if we want to set it to throughput in terms of products per minute we multiply the state percentage by the overall line rate in that state and add them together.

The line is down and not producing anything during the other 8.1% of the time.

So that’s how you calculate the throughput of a simple, non-linear packaging line. The calculations get more complex as you increase the number of machines, so later we’ll look at some shortcuts on how to cut down on the math. If you’d like one of our sales engineers to stop in a do a free line analysis for your packaging line, call us today.

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