Design of experiments

Once again, it's time to present the results of a Web search that uncovered more zero-cost, noncommercial, registration-free resources for your approval. The objective this month is practical information about the discipline called design of experiments (DOE), which is a highly efficient methodology for optimizing a multi-variable production process rapidly, using a minimum of data.

For example, DOE might apply to a conveyorized dryer. The general idea is to pack as much wet stuff as possible on the belt, pass it through the dryer only once as rapidly as possible to achieve a specific, identical part-to-part, minute-to-minute moisture content in each piece that exits the dryer. The relevant input variables might be temperature, spacing of wet items on the belt, conveyor speed, hot air flow and ambient humidity. A properly designed experiment minimizes the number of test runs needed to specify the best controller settings for the relevant variables. Then, with the hard work completed, operators need only tweak the settings a bit to pick up the last crumbs of operational improvement.

The research this month kept turning up references to somebody named Taguchi. So, we might as well start with a side search to learn about this person of apparently mythic proportions in the field of DOE.

Genichi Taguchi started making his impact on the American concept of quality in the early 1980s. You see, whereas it's common for us to speak in terms of the "quality" we've achieved, Taguchi speaks in terms of "quality loss" and the associated financial implications of reduced sales that occur when a process deviates from optimum. You can read his biography at several places. Try clicking over to http://www.skymark.com/resources/leaders/taguchi.asp or http://www.dti.gov.uk/mbp/bpgt/m9ja00001/m9ja0000111.html.

The concept of designing efficient experiments applies to more than manufacturing and hypothetical continuous dryers. Imagine for a moment trying to teach DOE to students who've never even been inside a manufacturing plant. It requires a different frame of reference that William G. Hunter at the University of Wisconsin-Madison has nailed down quite nicely. He forces his students to come up with their own experiments, many of which are listed online. I refer you to a document titled 101 ways to design an experiment. Or some ideas about teaching design of experiments. You can find it at http://www.stat.wisc.edu/department/handouts/technical413/technical413.html. The piece is rather long, so in the interest of your own surfing efficiency, I'd suggest you scroll to about half way down the document to get to the 101 experiments his students optimized. They include fireworks fuses, hitching a ride, melting sidewalk ice, baking biscuits and getting a letter delivered across the country.

Back on the industrial frontier, however, one might have an intense interest in the matter of selective reflow soldering. It's the joining of two solder-plated parts using localized heating. The relevant variables include heating rate, reflow temperature, time-at-reflow temperature, cooling rate, solder thickness, flux type and thickness, and heat sinking effects. The idea is to achieve the highest bond strength. It's merely another case of DOE to the rescue. You can read microJoining Solutions' Selective Reflow Soldering - Quality Assurance Issues - Solder Thickness and Flux Control at

http://www.microjoining.com/microTip_Solder&Flux.pdf.

DOE's great reliance on statistics means that it's necessarily a mathematically intense exercise. The best way to learn the process is to start with a simple problem. For example, you can read Communicating Design of Experiments to Non-Statisticians by Steve Schmidt and Ken Case. This article explains how DOE can be applied to rediscovering Newton's Law and Ohm's Law. It provides the fully worked-out mathematics for both cases. You'll find it at http://www.airacad.com/comdoe.htm.

Fast forward to a college-level course and you get Statistics in Research II, a class taught by Oliver Schabenberger, former instructor at Virginia Tech. He was kind enough to post his lecture notes at http://kitchen.stat.vt.edu/~oliver/stat5616/LectureNotes.html. Also, you might be interested in his glossary, which is found at http://kitchen.stat.vt.edu/~oliver/stat5616/handouts/DOEVocabulary.pdf.

You can find a slide show of the lecture notes for Design of Experiment and Robust Design, a course taught by Wayne Li from The University of Washington in Seattle. They cover only the high spots in what is probably an interesting class session, but it's rather sparse in terms of explanatory material. Nevertheless, I have no doubt you'll figure it out if you simply go with the flow and use your imagination. Li posts his material at http://courses.washington.edu/courseli/me355/Lectures/lecture19.pdf.

On the other hand, Barney Klamecki's page at the University of Minnesota is a little heavy on the math, but with just enough explanatory material to tie those numbers together into a coherent whole. You can read his Experimental Design Tutorial at http://www.me.umn.edu/courses/me3221-sum/Labs/Expdesign/