Joined: Sat Sep 06, 2014 8:05 pm
Posts: 37
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My Minions and I have been baking pellets and scoring them since The Great Restoration a week ago. I've been presumptive thus far that having all the ovens at the same settings (time, pressure and temperature variables) is a Good Thing with greater reliability, and more important, simplicity. Three independent variables produces a 4-D plotting with the 4th dimension being the dependent one (pellet score). Not possible to depict this with any great clarity in our 3-D Universe, unless you can animate one of the independent variables to show what happens to a 3-D surface depicting the other two independent (X and Y axes) with the dependent one (Z-axis) as the animated one is varied.
From reviewing the limited amount of data from my own experiments there may be more than one maxima among the three variables. In other words, it's not linear, with one or more of the variables quadratic or even cubic, which can result in multiple maxima. In addition I suspect interaction between at least two variables, i.e. if you change one variable it affects not just the score, but how another variable behaves and affects the score.
I wouldn't expect optimal pellet manufacturing to be a simple relationship between the variables. That would make it too easy for explorers to determine by simple trial and error, albeit a collective one sharing information, as in this extensive thread. Would also be much too easy for anyone familiar with basic statistical analyses, ANOVA and linear regression.
Having some experience in Experiment Design helps find at least one maxima quickly. I was initially presumptive that there is only one maxima, and at worst there would possibly be one quadratic variable (i.e. a variable squared), and perhaps one two-factor interaction (i.e. behavior of one variable depends on another variable's value). A little more complex would be the possibility of an otherwise linear variable having a point of discontinuity, that it's behavior might be linear but with a different slope on each side of a specific value, which might appear to be a parabolic quadratic and could be approximated as one.
I found one maxima, and it's a good one. Took only six runs to find values close enough to know I was in its vicinity. The technique used is called, in technobabble, a partial factorial design, followed by a method called "splitting the dictionary." I suspect it's not the best of multiple maxima, which may have shifted with one or more of the restorations. The one I've found thus far is in the vicinity of these values:
- Time: 25
- Pressure: 37.5
- Temperature: 37.5
- Mean Score: ~900
There is some interaction between Pressure and Temperature. Either can be increased slightly, but do not increase both together, nor decrease either of them (together or separately). For those seeking "short bake time" settings that return a high score, but not necessarily the highest, these can be used. Shift much from any of these in any direction and the score starts to plummet. It's a small peak in the solution surface.
For those who want more of the gory experiment design details:
The partial factorial was six runs with three levels for each of the three independent variables (time, press, temp). Doing a full 3^3 factorial would require just that, 3^3 or 27 runs and would be very time consuming to say the least. A well designed partial factorial can reveal quite a bit of information about the process at hand very quickly. I was down to values nearly on top of those above in just 18 runs, using what was learned from all prior runs to do additional partial factorials homing in on the maxima. (Getting into further details here would be lengthy and likely too much technobabble.)
I'm currently working on discovering if there are other maxima, and if so, what they are.
John
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