Posts Tagged design of experiments
Beware of 5th poly mole!
I found it amusing that, when forced to try modeling my weight data (see previous blog), my DOE software recommended a fifth order polynomial* model! That’s a bit more ‘tayloring’ (Ha ha – inside joke) than I really needed. In fact, just to show how silly this is (5th order!) I offer the following scenario as a cautionary tale. Perhaps it may help to dissuade others who make similarly nonsensical models from what is really just (naturally) randomly generated data.
Looking forward to a work/vacation trip to Tampa in late March (I really will be going there, I am happy to say!), let’s pretend that I use this fifth-order model to help me decide whether to bring a swimming suit. Hmmm, extrapolating out to day 75, when I finish my conference and head for the Gulf shore, the over-fitted model (really should just use the mean!) predicts that by then I will balloon to nearly 100 pounds over my norm. In this case I may easily be mistaken for a beached whale!
It’s just not right to apply model-fitting tools to what is not a DOE, but rather simply a process run-out at steady-state conditions. Extrapolation makes this even more dangerous by far. See the graph for a case in point.
*(A math-phobic person I am acquainted with, whom I will not identify, mockingly refers to these equations as “poly moles” — hence my title for this blog.)
Priming R&D managers to allow sufficient runs for well-designed experiment
Posted by mark in design of experiments on June 2, 2010
I am learning a lot this week at the Third European DOE User meeting in Lucerne, which features many excellent applications of DOE to industrial problems. Here’s an interesting observation from Pavel Nesladek, a technical expert from the Advanced Mask Technology Center of Dresden, Germany. He encounters severe pressure to find answers in minimal time at the least possible cost. Pavel found that whatever number of runs he asked to do for a given design of experiment, his manager would press for fewer. However, he learned that by asking for a prime number, these questions would be preempted, presumably because this seemed to be so precise that it must not be tampered with! For example, Pavel really needed to complete 20 runs for adequate power and resolution in a troubleshooting experiment, so he asked for 23 and got it. Tricky! Perhaps you stats-savvy readers who need a certain sample size to accomplish your objective might try this approach. Prima!
PB&J please, but hold the jelly (and margarine) and put it on toast – a mixture design combined with a categorical factor
Posted by mark in design of experiments, Uncategorized, Wellness on May 27, 2010
My colleague Pat Whitcomb just completed the first teach of Advanced Formulations: Combining Mixture & Process Variables. It inspired me to develop a virtual experiment for optimizing my perfect peanut butter and jelly (PB&J) sandwich. This was a staple for me and my six siblings when we were growing up. Unfortunately, so far as I was concerned, my mother generously slathered margarine on the bread (always white in those days – no whole grains) and then thick layers of peanut butter and jelly (always grape). As you see* in the response surfaces for overall liking [ 🙁 1-9 🙂 ], I prefer that none of the mixture ingredients (A: Peanut butter, B: Margarine, C: Jelly) be mixed, and I like the bread toasted. This analysis was produced using the Combined design tab from Design-Expert® software version 8 released by Stat-Ease earlier this year. I’d be happy to provide the data set, especially for anyone that may be hosting me for a PB&J dinner party. 😉
*Click to enlarge the plots so you can see the legend, etc.
Two-level factorial experimentation might make music for my ears
Posted by mark in design of experiments, Uncategorized, Wellness on May 9, 2010
I am a fan of classical music – it soothes my mind and lifts my spirits. Maybe I’m deluded, but I swear there’s a Mozart effect* on my brain. However, a big monkey wrench comes flying in on my blissful state when my stereo speaker (always only one of the two) suddenly goes into a hissy fit. I’ve tried a number of things on a hit-or-miss basis and failed to find the culprit. At this point I think it’s most likely the receiver itself – a Yamaha RX496. However, before spending the money to replace it, I’d like to rule out a number of other factors:
- Speaker set: A vs B
- Speaker wire: Thin vs Thick.
- Source: CD vs FM-Radio
- Speaker: Left vs Right.
It’s very possible that an interaction of two or more factors may be causing the problem, so to cover all bases I need to do all 16 possible combinations (2^4). But, aside from the work this involves for all the switching around of parts and settings, I am stymied by the failure being so sporadic.
Anyways, I feel better now having vented this to my blog while listening to some soothing Sunday choir music by the Dale Warland Singers on the local classical radio station. I’m taking no chances: It’s playing on my backup Panasonic SA-EN25 bookshelf system.
*Vastly over-rated according to this report by the Skeptic’s Dictionary.
Creativity defeats sensibility for paper helicopter fly-off
Posted by mark in design of experiments on April 9, 2010
Twice a year I teach a day on design of experiments (DOE) at Ohio State University’s Fisher College of Business. The students are top-flight executives seeking six sigma black belt certification. To demonstrate their proficiency for doing DOE, I ask them to break into teams of three or four and, within a two hour period, complete a two-level factorial on paper helicopters.*
It’s always interesting to see how intensely these teams from industry compete to develop the ‘copter that flies longest while landing most accurately. However, this year one group stood out as being less competitive than the others. Therefore, I was very surprised that they handily won our final fly-off. It turns out that one of their factors was dropping the helicopter either wings-up or wings-down – the latter configuration being completely non-intuitive. It turns out that going upside down makes it easier to drop, the flight time suffers only slightly and the flight becomes far more accurate – a premium in my overall scoring.
“The chief enemy of creativity is ‘good’ sense.”
– Pablo Picasso
Ironically, another team who benefited from having an expert in aeronautical engineering and a very impressive work ethic all around – they did more runs by far than anyone else – never thought of flying the ‘copters upside down. In fact, their team leader objected very vigorously that this orientation must not be allowed, it being clearly unfair. Fortunately, other executives in this black-belt class hooted this down.
I thought this provided a good lesson for process and product improvement – never assume that something cannot work when it can be easily tested. That’s the beauty of DOE – it enables one to screen unknown (and summarily dismissed) factors to uncover a vital few that often prove to be the key for beating the competition.
*I also do this experiment for a class on DOE that I teach every Spring at South Dakota School of Mines and Technology. In fact, I am writing this blog from their campus in Rapid City where I’ll be teaching class tonight. For details, pictures and results of prior experiments here and at OSU, see this 2004 Stat-Teaser article on “Playing with Paper Helicopters”.
Evolutionary operation
Posted by mark in design of experiments, Uncategorized on March 7, 2010
Last December, after an outing by the Florida sea, I put out an alert about monster lobsters. This reminded me of an illustration by statistical gurus Box and Draper* of a manufacturing improvement method called evolutionary operation (EVOP), which calls for an ongoing series of two-level factorial designs that illuminate a path to more desirable conditions.
With the aid of Design-Expert® software, I reproduced in color the contour plot in Figure 1.3 from the book on EVOP by Box and Draper (see figure at the right). To illustrate the basic principle of evolution, Box and Draper supposed that a series of mutations induced variation in length of lobster claws as well as the pressure the creatures could apply. The contours display the percentage of lobsters at any given combination of length and pressure who survive long enough to reproduce. Naturally this species then evolves toward the optimum of these two attributes as I’ve shown in the middle graph (black and white contours with lobsters crawling all over them).
In this way, Box and Draper present the two key components of natural selection:
- Variation
- An environment that favors select variants.
The strategy of EVOP mimics this process for improvement, but in a controlled fashion. As illustrated here in the left-most plot, a two-level factorial,** with ranges restricted so as not to upset manufacturing, is run repeatedly – often enough to detect a significant improvement. In this case, three cycles suffices to power up the signal-to-noise ratio. This case illustrates a big manufacturing-yield improvement over the course of an EVOP. However, any number of system attributes can be accounted for via multiple-response optimization tools provided by Design-Expert or the like. This ensures that an EVOP will produce more desirable operating conditions overall for process efficiency and product quality.
It pays to pay attention to nature!
*Box, G. E. P. and N. R. Draper, Evolutionary Operation, Wiley New York, 1969. (Wiley Classics Library, paperback edition, 1998.)
**(We show designs with center points as a check for curvature.)
Skepticism versus cynicism about science experiments
Eric Felten’s latest “De Gustibus” column in Wall Street Journal reports New Episodes of Scientists Behaving Badly. It details various scandals, for example the retraction of a landmark publication linking autism to childhood vaccines. This creates a great deal of cynicism such as that expressed by this parent of a kid she helped on a science project:
“The experiments never turned out the way they were supposed to, and so we were always having to fudge the results so that the projects wouldn’t be screwy. I always felt guilty about that dishonesty, but now I feel like we were doing real science.”
Ouch!
Coincidentally, Stat-Ease received an email from someone who goes by the pen-name “The Pyrrhonist.” (I see a trend here: I need to work on a scholarly-sounding moniker.) While researching pyrrhonism, I came across this skeptical quote by a Greek named Carneades who set the stage for his countryman Pyrrho:
“Nothing can be known, not even this.”
That’s tough to get around!
I truly believe that some degree of skepticism is healthy, such as judicious use of the null hypothesis for assessing the outcome of experiments. However, it’s not good for experimenters to abandon all standards by succumbing to an attitude of scornful or jaded negativity, especially a general distrust of the integrity or professed motives of others – the definition of cynicism (according to the Free Dictionary).
So, be skeptical, but not cynical.
Gambling with the devil
Posted by mark in Basic stats & math, design of experiments on November 15, 2009
In today’s “AskMarilyn” column by Marilyn vos Savant for Parade magazine she addresses a question about the game of Scrabble: Is it fair at the outset for one player to pick all seven letter-tiles rather than awaiting his turn to take one at a time? The fellow’s mother doesn’t like this. She claims that he might grab the valuable “X” before others have the chance. Follow the link for Marilyn’s answer to this issue of random (or not) sampling.
This week I did my day on DOE (design of experiments) for a biannual workshop on Lean Six Sigma sponsored by Ohio State University’s Fisher College of Business (blended with training by www.MoreSteam.com.) Early on I present a case study* on a training experiment done by a software publisher. The goal is to increase the productivity of programmers by sending them to workshop. The manager asks for volunteers from his staff of 30. Half agree to go. Upon their return from the class his annual performance rating, done subjectively on a ten-point scale, reveals a statistically significant increase due to the training. I ask you (the same as I ask my lean six sigma students): Is this fair?
“Designing an experiment is like gambling with the devil: only a random strategy can defeat all his betting systems.”
— RA Fisher
PS. I put my class to the test of whether they really “get” how to design and analyze a two-level factorial experiment by asking them to develop a long-flying and accurate paper helicopter. They use Design-Ease software, which lays out a randomized plan. However, the student tasked with dropping the ‘copters of one of the teams just grabbed all eight of their designs and jumped up the chair. I asked her if she planned to drop them all at once, or what. She told me that only one at a time would be flown – selected by intuition as the trials progressed. What an interesting sampling strategy!
PPS. Check out this paper “hella copter” developed for another statistics class (not mine).
*(Source: “Design of Experiments, A Powerful Analytical Tool” by Christopher Nachtsheim and Bradley Jones, Six Sigma Forum Magazine, August 2003.)
Awesome demonstration of design of experiments
Posted by mark in design of experiments on April 27, 2009
Team Awesome
The engineering students at South Dakota School of Mines and Technology really do rock. Where else could one present a class on statistics until 8:30 pm on a Friday night and continue it less than 12 hours later – early on a Saturday morning?
Our workshop on design of experiments (DOE) finished with a spirited competition of paper helicopters.* The winner was Team Awesome: Kayla Rithmiller, MacKenzie Trask and Samantha Johnson (pictured from left to right). They scored highest on the basis of flight time and accuracy. You can see their ‘copter spinning to another precise landing in their confirmation run.
Congratulations to Team Awesome and all the SDSM&T students who devoted their free time to learning DOE and demonstrating this newly-gained knowledge via well-planned experiments on the helicopter exercise. I predict that they all will go far!
*See details on this DOE exercise in the September 2004 Stat-Teaser article on Playing with Paper Helicopters.