My 'go to' experiential DOE learning tools were the paper helicopters and some version of the 'Statapult'. Back in my day of training Eastman Kodak Company Six Sigma Black Belts we used a custom designed and fabricated statapult that had a combination of discrete numeric (eg. number of rubber bands), continuous ( eg. arm length), and categorical factors (eg. ball type, like foam, solid plastic, plastic with holes). The team had to design their own measurement system. People did things like build a sand filled landing pit (think long jump pit) or two people estimating landing point along a tape measure, average the observations. The statapult was a great tool because it so much emulated real life in the lab or production. People got confused, it broke, nuisance variables galore, you name it it happened. One participant moaned about all the operational issues...another on their team told them something like, '...this is what happens in real life...learning how deal with these issues is half of what we're learning here...not just statistics'.
Another, more specialized choice was in our Measurement Systems Analysis module. At the end of the module we had teams set up a typical MSA study...which is still a designed experiment, just with special characteristics like nesting, crossing, replication, operators, devices, and on and on plus specialized analysis methods...which we focused on Wheeler's EMP approach. The teams were given a response...which was the 'length in inches of a plastic straw'. They were given multiple devices to assess length. Things like a plastic ruler, calipers, a micrometer, etc. Then told to define a measurement system and analyze the results using Wheeler's method. But we threw a few monkey wrenches at them. There were 4 or 5 straws that were the 'parts'. One straw had a beveled edge...so there was always lots of conversation about how to actually measure length...when one end of the straw has two distinct end points. One straw was too long to fit in the jaws of the caliper. One 'device' was delineated in metric...so they had to do a conversion to inches. This module was always lots of fun to watch the participants work through all the issues.