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Posted: Fri Jul 20, 2007 7:39 pm — Post subject: Pellet oven linearity
We've gotten a lot of information out of the ovens in the past month, but there are still basic principles that haven't really been hammered out. I decided to test a simple one: does the pellet score of a batch equal the sum of the pellet scores of the four ovens? In other words, do the ovens add linearly, or do their settings interfere with each other in some way?
(On Monday, IngisKahn said: "I can confirm that Amount has a purely linear effect." I wasn't sure what he meant, though, and he didn't cite any data.)
To test this, I tried various combinations of ovens being "on" or "off". "On," in this post, means an oven set to 30/30/30 (on the 0-50 scale); "off" means an oven set to .5/.5/.5 (the lowest the slider can be set without deactivating the oven system).
As is now well-known, if all ovens are "on" (30/30/30), you get a batch of pellets with an average KI score of 960-980 -- nearly as high as that measure can get. When they're all "off" (.5/.5/.5), you get completely unreactive pellets ("floaters") with a uniform KI score of zero.
I didn't try every combination, but here's what I got:
As you can see, this looks very much like a simple additive process. The value when ovens 1,2 are on is close to the sum of oven 1 and oven 2:
And the well-tested value (1,2,3,4) also fits this model. It should be the same as (1,2,3), since oven 4 contributes 0 at the 30/30/30 setting, and that's just what people find.
Caveats:
All the prediction errors were positive. In other words, all the measured values for multi-oven runs were just a bit lower than the sum of the ovens. This could be experimental error, or it could indicate a nonlinearity that doesn't get large until higher settings.
All of the pellets I tested were in the low ("floater") to middle (small and large "red ring") range. We know that the KI score drops off again for "white ring" and "exploder" pellets. I doubt that simple linear addition will remain true for those.
However, we might see a simple peak function, where the oven values add up to a certain limit (1000) and then subtract after that.
More on these tests later. I'm on vacation for the next week. :)
(On Monday, IngisKahn said: "I can confirm that Amount has a purely linear effect." I wasn't sure what he meant, though, and he didn't cite any data.)
To test this, I tried various combinations of ovens being "on" or "off". "On," in this post, means an oven set to 30/30/30 (on the 0-50 scale); "off" means an oven set to .5/.5/.5 (the lowest the slider can be set without deactivating the oven system).
As is now well-known, if all ovens are "on" (30/30/30), you get a batch of pellets with an average KI score of 960-980 -- nearly as high as that measure can get. When they're all "off" (.5/.5/.5), you get completely unreactive pellets ("floaters") with a uniform KI score of zero.
I didn't try every combination, but here's what I got:
Ovens ON: Average KI points per pellet (standard deviation)
1: 471.2 (8.2)
2: 266.6 (3.4)
3: 249.2 (4.2)
4: 0.0 (0.0)
1,2: 729.0 (8.2)
1,3: 705.2 (11.0)
1,4: 463.2 (7.2)
2,3: 513.4 (7.5)
1,2,3: 971.2 (16.0)
As you can see, this looks very much like a simple additive process. The value when ovens 1,2 are on is close to the sum of oven 1 and oven 2:
Ovens ON: Measured points : Predicted points (error)
1,2: 729.0 : 737.8 (+1.2 %)
1,3: 705.2 : 720.4 (+2.2 %)
1,4: 463.2 : 471.2 (+1.7 %)
1,2,3: 971.2 : 987.0 (+1.6 %)
And the well-tested value (1,2,3,4) also fits this model. It should be the same as (1,2,3), since oven 4 contributes 0 at the 30/30/30 setting, and that's just what people find.
Caveats:
All the prediction errors were positive. In other words, all the measured values for multi-oven runs were just a bit lower than the sum of the ovens. This could be experimental error, or it could indicate a nonlinearity that doesn't get large until higher settings.
All of the pellets I tested were in the low ("floater") to middle (small and large "red ring") range. We know that the KI score drops off again for "white ring" and "exploder" pellets. I doubt that simple linear addition will remain true for those.
However, we might see a simple peak function, where the oven values add up to a certain limit (1000) and then subtract after that.
More on these tests later. I'm on vacation for the next week. :)
_________________
Andrew Plotkin (KI#00102725)
Uru Newcomer's Guide and Answer Sheet
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