Design-Expert® software version 12 (DX12) released this summer with a cool new tool to model binary responses, for example, pass-versus-fail quality-testing. For what it’s worth, the methodology is called “logistic regression”, but suffice it to say that it handles results restricted to only two values, typically 0 or 1. The user deems which level is a success, most often “1”.
During development of DX12 Stat-Ease moved to a penthouse office on a building with a cascade of balconies. So, when our programmers, led by Hank Anderson, considered how to test this feature with an experiment, they came up with the idea of trying various packing on eggs to see if they could be dropped some distance without breaking—a project that high-school science teachers assign their students. However, we figured that our neighboring tenants down below and our new landlord might not be very happy about the mess that this would create. Therefore, Hank and his team took a less problematic tack by testing various factors for microwaving eggs to an edible stage. This experiment (or ‘eggs-periment’ if you like) also was more productive for varying the diet of the programmers from their staple of boiled ramen noodles—the focus of a prior DOE.* If they could achieve consistent success in cooking eggs by microwave, a combination of these with ramen might be the ideal sustenance for awesome coding for new versions of Design-Expert.
The Stat-Ease experiment began with a bang during the range-finding stage with an explosive result. You might say that the yolk was on us—bits of overcooked egg and shell dispersed throughout the chamber of the microwave. The picture below shows the messy aftermath (note the safety glasses).
After this learning experience (‘eggs-perience’?), Hank and his lab technician, Mike Brownson, settled into a safer range of factors, shown below, that kept the contents from reaching the catastrophic breaking point:
- Preheat—0 to 180 seconds
- Cooking time—120 to 420 seconds
- Power—60 to 100 percent
- Salt—0 to 2 teaspoons
- Egg Size —Large or Jumbo
Hank and Mike, with input from Stat-Ease Consultant Martin Bezener, put together an ambitious design with 92 runs using Design-Expert’s custom design builder (i-optimal) for response surface methods. Heads-up: When responses are restricted to just two outcomes (binary), many more runs are required to provide adequate power than would be required for a continuous measure.
The investment of nearly 100 trials for the ‘eggs-periment’ paid off by producing significant results on pass/fail measures of undercooking and overcooking. For example, the 3D graph below shows the probability of eggs being undercooked as a function of time and power for the microwaving. Notice by the corner at the left being cut off that potentially catastrophic combinations of high power and long cooking were excluded via a multifactor constraint. Clever!
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Based on models produced from this experiment, Design-Expert’s multiple-response optimization recommends a most desirable setup for microwaving eggs as follows: Heavily salted jumbos preheated to the maximum level and then cooked for 315 seconds at medium power.
Thanks to the research by Hank, Mike and Martin, our programming staff now is fueled not just by ramen, but also with eggs—a spectacular success for DX12’s new logistic-regression tools!
* “The Optimal Recession-Proof Recipe”, Brooks Henderson, pp 1-2, September 2012 Stat-Teaser, followed up by “Confirming the Optimal Ramen”, p3, January 2013 Stat-Teaser.