Conveyor Blog

Non-Linear Throughput Analysis of a Packaging Line

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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.

State Percentage of Time Max Rate (ppm) Throughput
1 83.14% 500ppm 415.7 products
2 4.38% 300ppm 13.14 products
3 4.38% 300ppm 13.14 products
Total 91.9%   441.98 products per minute

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.

Put Those Bugs to Work

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Scientists in Korea have figured out a way to circumvent the costly production of polylactic acid (PLA), which is used in the production of biodegradable, eco-friendly plastics. They’re using E. Coli bacteria. .

Before, we had to go through a two-step fermentation and complicated chemical process of polymerization. This time, we metabolically engineered E. coli and fed it with biomass. Then PLA could be accumulated right away in the E. Coli cells, ending up with a one-step process.”

E. Coli can help produce plastics

Tradition: The Garvey Gong Show

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Every year we all get together and have a holiday luncheon the last work day before Christmas. We invite retirees, welcome new people who we’ve hired recently, and talk about our goals and performance for the year. One year my Dad decided that there was too much talent the room to let it go to waste, so he created the Garvey Gong Show. Three judges are chosen and the rest of the employees get up and perform any kind of talent they have, whether it’s telling jokes, playing music, karaoke, ventriloquism, etc. Today is the 8th Garvey Gong Show and it’s something I look forward to every year.

The contestants are warming up

The contestants are warming up

Great Grocery Store Photo

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I saw this photo on the Packaging Diva Blog today. It gives you a sense of the immensity of the packaging industry.

A familiar sight from an unfamiliar angle

A familiar sight from an unfamiliar angle

Conveyor Considerations: Speed, Safety, and Sanitation

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Food and Beverage Packaging Magzazine posted an article today where they quoted various luminaries of the conveyor industry about speed, safety, and sanitation. They also quoted me.

Garvey general manager Ben Garvey concurs. “For us, the biggest difference between food and beverage markets is the speed—beverage lines run two to four times faster than a typical food packaging line. Overall conveyor construction is similar, because of contamination concerns. They all require easily cleanable conveyors.”

Read the entire article here.

Great Wine Barrel Pic

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Practical Winery and Vineyard’s latest cover story has a great shot of the huge wine barrels made by Oak Cooperage.

Practical Winery and Vineyard

Practical Winery and Vineyard

We have installed many of our Infinity tables in the wine industry in California and Australia. They raise throughput by protecting fillers from downtime on labelers and casepackers.

Conveyor Belt of Love

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QC Industries beat me to it this morning, but it’s not too often that the word “Conveyor” is in a network TV show. Something tells me it may not be around for very long. Check out ABC’s Conveyor Belt of Love:

Yes, really. ABC is airing a show called “Conveyor Belt of Love” on Jan. 4, right after the premiere of “The Bachelor.”

And if you’re wondering what a show called “Conveyor Belt of Love” would entail, well, the title succinctly and depressingly pretty well says it all. From the network’s press release: “One by one … 30 men are presented on the ‘Conveyor Belt of Love’ to … five women and given 60 seconds to impress them. If a woman is interested in someone, that man will step aside and wait as the rest of the men go by.”

This isn’t the first or the last time conveyors play a role in mainstream culture. James Bond always seems to be fighting a bad guy on one and of course, everyone remembers the classic episode of I Love Lucy.

Vial Accumulation Table

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We’ve been posting some more videos on YouTube lately as an alternative to the ones here on our website. Here’s a great one we just posted of our Infinity Rx vial accumulation table.

It shows how we can take very unstable pharmaceutical vials and single file them to feed a filler, labeler, or inspection machine.

Evaluating the Total Cost of Ownership

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Alan over at the Sustainability in Packaging blog made a great post about how to evaluate the True Cost of Cheap Equipment:

The seemingly lower purchase price, although deceptive, is not malicious in nature. The omission of regulatory compliance or the absence of IOQ document costs stem mostly from where the vendor stands on the evolutionary timescale vis à vie the market they are entering. The onus therefore is on the buyer to encompass non-trivial costs in their analysis—costs which exceed the mere functioning of the machine.

Beware of hidden costs

Beware of hidden costs

One simple way to evaluate how high your total cost of ownership will be for a machine is to ask the vendor what percentage of his business is in spare parts.

Usability Problem

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I love little examples from every day life that show good or bad design that can be related back to well designed machinery. On the machinedesign.com blog, Leslie Gordon gives a great example of poorly thought out usability in an elevator alert light. It’s supposed to show which elevator is about to open, but because of the column, you can see the light.

We can't see the light behind the column

We can't see the light behind the column

This happens when designers and engineers work inside of a bubble. They worked on a perfectly useful feature that is rendered less useful in the context of the structure around it. This happens all the time in our industry where a typical automated packaging line consists of machines designed by many different vendors. How can we make sure our features are still useful in the context of where they’ll be installed? What are some good design practices to use to achieve this?