Design of experiments

It's a way to ensure that every hard-won data point expresses its full measure of value

By Russell L. Kratowicz, P.E.

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.

Everyday examples

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.

The nitty-gritty

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/

expdesign.html.

But if you really want to get into the mathematics of statistics, the must-see online resource is the Engineering Statistics Handbook. This prodigious work shows you how to explore, measure, characterize, model improve, monitor and compare data sets using every statistical tool known to mankind. The work is heavily linked and interlinked, so there's no way to determine the document's length easily. Take my word for it, there's a lot of material here. Bookmark http://www.itl.nist.gov/div898/handbook/ if you need to do any work with statistics.

Thinking about experiments

Now that you've gotten the general drift of DOE, it's time to explore the thought process that goes into setting up an experiment. Stacy Gleixner at San Jose State University teaches a course on semiconductor manufacturing and, as you would expect, there are quite a few variables involved in building a chipset for your latest wireless whirlygig. It's no wonder that DOE is such an important tool in Silicon Valley. Gleixner posted a set of lab notes online and I'd like to direct your attention to Lab 4 and Lab 5. The first shows how to think about an experiment to identify the effect a single variable has on a process. The second deals with the effect of multiple variables. Point your trusty silicon browser to

http://www.engr.sjsu.edu/sgleixner/mate166/lab_handouts.htm and learn how to think experimentally.

Your tax money at work

Even the military is interested in designing experiments properly. That's not surprising, considering the fact they play for keeps using real bullets. The Department of Math Sciences at the U.S. Military Academy, West Point, N.Y. also shows you how to think about the experiment, but with a bit more emphasis on the results. Be sure to click your way to Design of Experiments, which is found at

www.dean.usma.edu/math/courses/ma376/handouts/Ma376_11.ppt. This PowerPoint presentation makes reference to something identified as Ho and Ha. In the branch of statistics called hypothesis testing, these correspond to the null hypothesis and alternate hypothesis, respectively. Gosh, that sounds like a topic for a future column.

The freebies

As you may have gathered by now, DOE is computationally heavy. In fact, with so much statistics involved, making sense of it is a job perfectly suited for digital processing. And I'm happy to report that, in their desire to make your foray into DOE as painless as possible, several Web sites offer you suitable software, some of which is free.

The first resource is found on the Process Quality Management Web site, which comes to you out of the Czech Republic. Specifically, I direct your greedy, acquisitive mouse to

http://www.pqm.cz/Engpqm/frsoftware.htm#free%20software, where you will find something called Five Easy Steps To Solving Production Problems. The package is suitable for DOE problems that feature four, five or six two-level factors. First, read through the worked-out example to be sure that your problem matches the capabilities of this DOS-based software package. Yes, that's rightDOS. But, it's free. What do you want?

The next offering by Peter Bruce of Bruce Advertising brings you Statistics.com, a worthwhile site for all your statistical needs. Start with the free software downloads. There are no less than 40 totally free statistical software packages covering the full gamut of calculations needed to excel in this discipline, including DOE. Merely having the tools, though, is pointless unless you know how to use them effectively. So, while you're there, check out the online textbooks, a link to which is found on the left side of the page. Aim your avaricious mouse to http://www.statistics.com/content/freesoft/AZlisting.html to capture the goods.

Rainer Wrlnder, IT manager with W.L. Gore & Associates near Munich, Germany, also publishes a list of software resources, some of which are free. The others are shareware, which means it's appropriate to trot out our standard caveat that applies to any shareware presented here.

Shareware relies on the honor system. If you download and use it, you're expected to compensate the software developer. Details are downloaded with the files. Now, go visit Wrlnder 's page titled Statistical Software at http://ourworld.compuserve.com/homepages/Rainer_Wuerlaender/statsoft.htm and play nice.

So retro

Before you leave, don't forget the related columns that appeared here in past issues. A two-parter on quantitative methods started in October 2000 and finished in January 2001. Also, a column on statistical process control appeared in the February 2001 issue. Both are available on the Plant Services Web site, which is found, amazingly enough, at http://www.plantservices.com.


Rusell Kratowicz is executive editor of Plant Services magazine. E-mail him at rkratowicz@putman.net.

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