Joined: Sat Sep 06, 2014 8:05 pm Posts: 37

Er'cana pellet production is essentially a manufacturing process that is ostensibly controlled by Time, Pressure and Temperature. These descriptors are arbitrarily presumptive from the symbols, and it matters not one iota what they actually are, if one or more be something different. These are merely labels for them. Aside from completing the combination of Er'cana and Ahnonay using a pellet drop to properly illuminate the lower Bahro cave and reveal the Cleft imager "code," it's my understanding Kadish created Er'cana to harvest materials and produce pellets to feed the lake algae and illuminate the Uru cavern. The pellet efficacy tool gives a numerical score for each pellet that's placed in it, and the higher the score, the better the pellet is for the Uru cavern lake and resulting illumination. Even if this isn't entirely accurate, higher scores are considered "better."
The goal then is to find settings for Time, Pressure and Temperature that will maximize the pellet score. One could try various combinations of settings to see what happens, and seek the optimal directly by trial and error. That's usually not very efficient, nor is it conducive to creating a mathematical model that can predict the score for a specific control settings, whether or not they've been used before. A structured approach to characterizing the process and creating a model for it is much more efficient and ultimately should be much more effective. Thus, the effort at the outset is to obtain data that can be used to characterize process response (pellet score) to control settings and not to directly find the optimal ones. The first step is a set of "screening runs" to determine whether each control affects pellet score, and to determine if there may be interactions between controls (i.e. one control setting changes how another affects process response). The customary method is selecting a "high" and "low" setting for each control and designing an experiment performing a series of "runs" using them. The absolute control limits could be used (in this case 1 and 50) but that is generally inadvisable. My personal, professional experience doing these analyses in real life has reinforced that. Could have used 5 and 45 for each, but decided to bring them in a little more to 10 and 40.
From an experiment design perspective, there are 3 controls and if we use two levels for each, there are 2^3 = 8 combinations for a full factorial. However, we don't need to run all 8 to learn something about the process. We can run half of them in a specific halffraction design of 4 runs called a Latin Square and still learn quite a bit. That we get 5 pellets from each run eliminates the necessity to perform "replications" of each run, provided we have confidence the process is reasonably stable (i.e. repeatable). Results might vary for another run using the same settings, but it is presumed that variance will be insignificant compared to the effect changing settings will have. If it isn't stable, then doing any experimentation, structured or otherwise, is utterly futile and the first goal in real life is stabilizing the process to make it reasonably repeatable. There could be a 3way interaction among all the settings, but that would be rare indeed (in real life). The Latin Square used confounds any 3way (time, press, and temp) interaction across the main effects individually and any of the three possible 2way interactions there might be among pairs of them. The four initial runs used the following settings:
Time Press. Temp.
10  10  10 10  40  40 40  10  40 40  40  10 In experiment design jargon, this type of design is called "orthogonal." Note that each level for each control occurs twice, and the combination used for any two control settings is not repeated (e.g. Time = 10 and Temp = 10 occurs once, and only once). The first discovery made was finding a "process edge" or boundary. Run number 3 with time and temperature both set to 40 resulted in a zero score. This is not good as it's considered a process "failure." A fifth run done with time, temperature and pressure all set to 40 also resulted in a zero score, another process failure. The problem, if 40 is used for the high level of Time and Temperature, is not knowing how far below that the two must be paired to produce a score greater than zero, even if it's tiny. A sixth run using 37.5 for Time and Temperature (with 10 for Pressure) resulted in a nonzero score. The other two runs with Time and Temperature set to 40 were rerun using 37.5 with the following results, averaging the scores for the 5 pellets produced in each run.
Time Press. Temp. Avg. Score
10  10  10 ==== 14.6 10  40  37.5 == 297.2 37.5  10  37.5 == 34.0 37.5  40  10 === 793.4 Rather than stare at a table of numbers trying to visualize what they mean, graphs can show very quickly how the different settings affect process response. The following three graphs were generated using this data to examine time, pressure and temperature from three different perspectives:
Of interest is the second graph which shows, quite compellingly, an interaction between Time and Temperature. If Time is low, increasing temperature increases the score. However, if Time is high, increasing temperature plummets the score, exactly the opposite effect. So, in eight runs we have found:
 A process boundary
 All three controls are significant (they all affect score)
 An interaction between the Time and Temperature settings
Dealing with the process boundary consumed four of the eight runs.
Because of the interaction, it would be useful to do the other half of the factorial to better understand (and completely confirm) the TimeTemperature interaction. The data already accumulated can be reused, requiring only four runs. That will be done in Part II.
John

