[scientizscht (OP)]

Hello

We have a factory with workers who process process potatoes.

When the factory is loaded with 1,000 potatoes, the workers take 1h to process a potato on average.

The next day, the factory is loaded with 1,200 potatoes and the workers take 1.2h to process a potato on average.

As you can see, the performance of potato processing as expressed by the average time to process a potato depends on the loading of the factory with potatoes.

However, the average processing time of a potato divided by the number of loaded potatoes stays the same at 0.001h/potato^2.

Does the above metric make sense and can it be used to assess the productivity of the factory after you exclude the effect of its potato loading? Is dividing an average with the total number of units a valid metric to compare the average between days of various total numbers of units?

If you do not use this metric, you will say that the second day, the processing time of the factory was 1.2h/potato which is 0.2h/potato less than yesterday so you will be worried that the performance has dropped and there is an issue while in fact it can be a 'natural' drop of performance due to higher load and no other issue would exist.

Any ideas?

If the metric makes sense, what are the implications if the relationship between loading and the average processing time is not linear?

Thanks!

[alancalverd]

It is difficult to see why it should take longer to process one potato if you have more in the store. This is a factory, not a government office.

Unless, of course, the factory is owned by a politician's family, in which case the actual processing of potatoes is irrelevant because the Minister can say "I have set a wordbeating target, which we met yesterday", whether or not the factory is actually capable of processing more than one potato per hour. Meanwhile, chip shops are going out of business....

[evan_au]

Does an average divided by the total make sense?

I have seen an application for the inverse: Total/Average.

I observed in a factory (many years ago) a worker counting out tiny items (small screws, maybe?).
- They counted out exactly 100 items, and weighed that, to get an average mass.
- The scale stored the average mass
- Then, if a particular production run needed exactly 1,234 of these items, the worker poured roughly the right volume onto the scale
- The scale measured the total mass, then divided by the average mass, displaying the exact quantity of items on the scale
- The operator could then add or remove a couple to give exactly the right quantity.

I am sure this would be all totally automated, these days...

[Colin2B]

Thanks for the feedback and extra detail on the problem.

Does the above metric make sense and can it be used to assess the productivity of the factory after you exclude the effect of its potato loading? Is dividing an average with the total number of units a valid metric to compare the average between days of various total numbers of units?

This is going to depend a great deal on the items you are working with. In the example @evan_au  gives it is reasonable to assume a relationship between the number of pieces to be scanned and the time taken to select a piece and place it. With potatoes it is harder to imagine what in the larger quantity would cause a difference.
Remember, what you are measuring here is not productivity.

If you do not use this metric, you will say that the second day, the processing time of the factory was 1.2h/potato which is 0.2h/potato less than yesterday so you will be worried that the performance has dropped and there is an issue while in fact it can be a 'natural' drop of performance due to higher load and no other issue would exist.

You should worry, in the sense of trying to work out why, because performance really has dropped. Is it because more staff breaks are needed and the spacing of the breaks is now uneven giving a false average comparison? What if you disregard break times. Are the workers aware of the larger quantity and become disheartened, thus slowing down? Whatever is happening needs some analysis to work out why.