In the late 1970’s I took an eveningcourse in marketing en route to myMBA. In class we worked through acase study showing how the nationalbeer brands in the USA, although theydiffered very little in their brews, hadmarketing campaigns that divideddrinkers into distinct segments. Forexample, Miller advertised their high-priced product as the ‘champagne’ ofbottled beer while Old Milwaukee wentfor the working man and took the lowroad on price. Meanwhile, on my dayjob as a chemical process developmentengineer, an R&D colleague made a bigdeal over how you got what you paidfor in beer: The cheap stuff was simplyswill in his opinion.

At this time I was gaining a greatappreciation for experiments based onstatistical principles, such as use of thenull hypothesis for reducing prejudice.Here was an opportunity to put the beersnob to the test via a blind, randomizedstatistically-planned experiment. You

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Workshop ScheduleA B O U T S TAT - E A S E ® S O F T W A R E , T R A I N I N G , A N D C O N S U LT I N G F O R D O EPhone 612.378.9449 Fax 612.378.2152 E-mail info@statease.com Web Site www.statease.com

September 2007 • 1

can guess the outcome: He rated theOld “Swill”waukee (his misnomer)number 1!

In the decades since this experiment alot has happened on the beer front, suchas the advent of microbrews. Much alsohas happened in the design of experi-ments (DOE) field, for example com-puter software for design and analysis ofmixture experiments. During theseyears my wife and I have raised fivechildren, the oldest of which, Ben, cele-brated his 28th birthday this summer.

Ben’s done some bartending and gainedsubject-matter knowledge on beers.His younger brother Hank enjoys agood brew, too. Therefore, neither oneof my two sons declined the opportuni-ty to become taste testers for a new

Mixture Design Brews Up NewMixture Design Brews Up NewBeer Cocktail—Black & Blue MoonBeer Cocktail—Black & Blue Moon

—Continued on page 2

Experiment Design Made EasyOctober 9–11, 2007: Minneapolis, MNDecember 4–6, 2007: Minneapolis, MNJanuary 22–24, 2008: San Diego, CAFebruary 12–14, 2008: Minneapolis, MNStudy the practical aspects of design ofexperiments (DOE). Learn about simple,but powerful, two-level factorial designs.$1495* ($1195 each, 3 or more)

Response Surface Methods for Process OptimizationNovember 13–15, 2007: Minneapolis, MNFebruary 26–28, 2008: Minneapolis, MNMaximize profitability by discovering optimal process settings via RSM. $1495*($1195 each, 3 or more)

Mixture Design for Optimal FormulationsOctober 23–25, 2007: Minneapolis, MNJanuary 29–31, 2008: Minneapolis, MNFind the ideal recipes for your mixtureswith high-powered statistical tools.$1495* ($1195 each, 3 or more)

DOE for DFSS: Variation by DesignNovember 7–8, 2007: Minneapolis, MNMarch 11–13, 2008: Minneapolis, MNUse DOE to create products and processesrobust to varying conditions, and tolerance analysis to assure yourspecifications are met. A must forDesign for Six Sigma (DFSS). $995* ($795each, 3 or more)

PreDOE: Basic Statistics forExperimenters (Web-Based)PreDOE is an entry-level course for thosewho need to go back to the basics. Seehttp://www.statease.com/clas_pre.htmlfor more information. $95

*Includes a $95 student materials chargewhich is subject to state and local taxes.

Attendance is limited to 16. Contact Eliciaat 612.746.2038 or workshops@statease.com.

©2007 Stat-Ease, Inc. All rights reserved.

Mark Anderson mixing up a new beer cocktail

A: Blue M oon60

B: Budw eiser60

C: Sam Adams B lack Lager60

0 0

0

2 2

2

2

Fig. 1: Augmented simplex lattice

2 • September 2007

experiment aimed at developing a beercocktail concocted from:

A. Blue Moon wheat beer ($1.16)B. Budweiser ($0.84)C. Sam Adams Dark Lager ($1.23).

(The prices per 12-ounce serving areshown in parentheses.)

Joining Ben and Hank was my son-in-law Ryan—born and raised in theMilwaukee area, where beer and milkare the preferred beverages. (I oncetried blending milk into beer. Do nottry this at home.) My only excuse forchauvinistically excluding daughtersand other ladies was that for scientificcontrol purposes this experiment had tobe restricted to twenty-something males.

Why these three beers you ask? I admitto being creative when browsing thebrands on the liquor store shelves. Mygut feeling was that something mightcome of this particular trio, but mainly Iwanted a contrast in tastes and prices,thus increasing the likelihood of some-thing significant occurring—for betteror worse. I can just see my old beerbuddy getting after me for even consid-ering the idea of mixing beers, but thisidea goes back hundreds of years towhen bartenders blended porters fromkegs kept under the counter, ideallyallowing cheaper ales to be siphoned offwith no objection by the drinkers.

For the DOE I used Design-Expert®software, version 7.1 (DX7.1), to set upan augmented simplex-lattice design.*

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Via the equation-only feature in DX7.1,I added cost per serving as the fourthresponse (Y4). If one wanted to reduceexpenses, mixing in a cheap amber lagerlike Budweiser would help as you cansee in Figure 3. The flag shows the cen-troid blend with equal measures of allthree beers. I cannot build up muchenthusiasm for this—too much workand not first-class. Perhaps I betraymyself here as an elitist when it comesto the finer things in life, such as a coldbeer on a hot evening sitting on the backporch after a long, hard day at theoffice.

If you’d like to see my data, e-mail me.However, I encourage you who enjoy asip of beer or other beverages to do yourown blending experiments. My thoughtis to try some Sangria wines whenthings start getting really hot. I enjoyedsome nice ones in San Juan over Springbreak! Perhaps the environment playeda role in my level of enjoyment—food(beverage) for thought.—Mark (mark@statease.com)

*(Learn more about mixture design byattending the three-day computer-intensive workshop, "Mixture Designfor Optimal Formulations." For a com-plete description of this class, seehttp://www.statease.com/clas_mix.html.Link from this page to the course out-line and schedule. The next class isOctober 23–25, 2007 in Minneapolis.Enroll online or by contacting Elicia, at612.746.2038 or elicia@statease.com.)

—Continued from page 1

Aided by the program’s design editingtools, I shifted replicates from the ver-tices (pure beers) to binary blends,which interested me most. The loca-tion of the resulting design points canbe seen in Figure 1 (on page 1).

The 14 blends per person (blocked)were provided in random run order forthese three sensory responses:

Y1. Taste on hedonic scale of 1 (worst) to 9 (best)—blindY2. Appearance (1–9)Y3. Overall liking (1–9)

I own a very accurate kitchen scale thatI use to weigh out green coffee beans forroasting (another story!) so it was con-venient to set the total for each blend to60 grams—roughly two fluid ounces.That kept the total beer consumption perperson to a reasonable level, about twobottles each. (During the experiments I,the mixologist, managed to drink aboutthe same amount—in the name of sci-ence, naturally. ☺) Each drinker kept hisown beer-shot glass, which they man-aged to empty after every run.

The results were very interesting as youcan see by the 3D response plot (seeFigure 2): A blend of Blue Moon (A)and Sam Adams Black Lager (C) really(p<0.01) hit the spot for overall liking!Taste and appearance ratings alsofavored this binary blend. The tastersall liked this combination, which I’vedeemed the ‘Black and Blue Moon’ beercocktail.

It is easy to break down the analysis byblock with the ignore-run capabilityprovided by Design-Expert. I foundthat the individuals differed somewhatin their tastes, for example, Ben dislikedBud, but Ryan did not mind this cheap-er beer. However, in my judgment itseemed best to pool all three tasters forthe power it provided in detecting thenonlinear blending effects.

A: Blue Moon60

B: Budweiser60

C: Sam Adams Black Lager60

0 0

0

Overall liking: 5.5

Cost: 1.10

3

66

6

3

3 3

6

3 3

Overall liking: 5.84282Cost: 1.07875X1 20X2 20X3 20

A (60)

C (60)

C (0)

3

4.25

5.5

6.75

8

Ove

rall

Likin

g

A (0)

B (60)

Fig. 2: Response surface shows peak Taste Fig. 3: Sweet spot for Taste

September 2007 • 3 Stat-Teaser • News from Stat-Ease, Inc.

No More Under-Sized Factorials via Shari’s Favorite New Tool (Part 1 of 2)

What would you say if a DOE programcould guarantee that your designs wouldalways be properly sized to find youreffects? No doubt you would appreciatethat it eliminates one of the most fre-quent causes of failed DOE’s! Well, wecan’t go so far as to make a guarantee,but version 7.1 of Design-Ease (DE) andDesign-Expert (DX) software does offera new tool that will really help you withfactorial designs. Called “up-frontpower,” it is incorporated into thedesign-build process, on the screenwhere you enter responses (see Figure 1).

Besides entering the response namesand units on this screen, you canoptionally enter the minimum changein the response that the design shoulddetect as significant, and the estimatedstandard deviation for that response.The standard deviation part is easy.It’s likely that you have some historicaldata sitting around somewhere thatyou can use to make a quick calcula-tion. The difference to detect comesfrom business knowledge. Here’s anexample: Everyone wants to maximizeYield—the higher, the better. But ifyou are operating at, say 80% Yieldtoday, what is the change in Yield thatwould make your boss take notice—

1%, 3%, 5%? Only you can answer thatquestion. Let’s say 3% was reasonable.With an estimated standard deviationfor the Yield response of 1%, Stat-Easesoftware calculates the signal-to-noiseratio to be 3/1 = 3.

If you provide this signal and noiseinformation, then pressing Continuewill bring up the power informationscreen (see Figure 2). Power is the abili-ty of a specific design to detect an effectof a certain size relative to the noise inthe process. It is recommended thatpower be approximately 80% or higher.For Yield, the power is great—99.9%probability of detecting a change inYield that is 3% or larger (if it exists!).You can use this design with confidencethat it will do the job for you.

What if power is too low? That will bethe topic of Part 2 of this article in thenext edition of the Stat-Teaser newslet-ter. If you can’t wait, and you have acopy of Design-Ease or Design-Expertsoftware, check the Help System. Go toHelp Contents / Design Evaluation /Interpretation of Power. Read this, thenfollow the link to “Not EnoughPower.” If you don’t already have acopy of DE or DX software, downloada free 45-day trial version athttp://www.statease.com/software.html.

Learn more about power for factorialdesigns by attending our “ExperimentDesign Made Easy” workshop. Asalways, feel free to e-mail questions toStatHelp@statease.com.—Shari Kraber (shari@statease.com)

Come & See Stat-Ease at Upcoming Events!

51st Fall Technical Conference, Jacksonville, FL, October 11–12, 2007, BoothTalk by Pat Whitcomb, October 12, 2007, "Graphical Selection of Effects in General Factorials"

MN Quality Conference, Bloomington, MN, October 15–16, 2007, BoothWorkshop by Shari Kraber, “DOE for DFSS,” & Talk by Mark Anderson, "DOE for Ruggedness Testing"

MD&M Minneapolis 2007, Minneapolis, MN, October 17–18, 2007, Booth 1149

ISMI Symposium on Manufacturing Effectiveness, Austin, TX, October 22–25, 2007, Booth Talk by Mark Anderson, "Dual Response Surface Methods (RSM) to Make Processes"

13th Annual International Validation Week, Philadelphia, PA, October 23–25, 2007, Booth

Design & Analysis of Experiments DAE2007, Memphis, TN, October 31–November 3, 2007, BoothSoftware Demo and Poster Session by Wayne Adams, “Methods for Sizing Designed Experiments”

Fig. 1: New Response Entry Screen

Fig. 2: Power Information Screen

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In August, Productivity Press released the second edition of DOE Simplified: Practical Tools forEffective Experimentation. This updated text by Anderson and Whitcomb offers a new chapter on thekeys to setting up a good design of experiments (DOE) through a four-step planning process, includ-ing assessment of statistical power. DOE Simplified covers all of the essentials needed to get you off toa good start on your own designed experiment and is filled with interesting anecdotes and sidebars thatmake it fun to read. Included is a 180-day educational version of Design-Ease® 7.1 software.

(Note: We are clearancing out the 1st Edition at 1/2 off—$22.50. If you would like to purchase the 1stEdition instead, please note it clearly when placing your order.)

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