beer foam

8/11/2019 Beer Foam

1/25

Experimental Design of Beer Foam Height

IEE572 Term Project

Instructor: Dr. Douglas C. Montgomery

Project Team:

Serhan Alshammari (1:30pm),Jinsung Cho (4:30pm),Tracy Lenz (1:30pm)

8/11/2019 Beer Foam

2/25

IEE 572 Project Height of Beer Foam

Serhan Alshammari, Jinsung Cho, Tracy Lenz Page 2

EXECUTIVE SUMMARY

Brewing and serving beer is a cultural and social subject in the United States. The chemistry andquantitative subject matter is organized by the American Society of Brewing Chemists, anorganization ASBC is a professional organization of scientists and technical professionals in the

brewing, malting, and allied industries . There was interest on behalf of a local brewer, BJsBrewery, to determine if an additive Biofoam CL could increase the foam head of a beer and ifso, under what conditions. BJs Brewery also wanted data on temperature and pressure.

The above photo is the laboratory for BJs Brewery. There are 5 major steps in the brewing process.

1. Malted barley is mixed with hot water to 65 to 75 Celcius. This is called mashing.

2. Lautering is a filter process to remove husks left over from the grains.3. Sparging is then completed. A liquid is sprinkled over the top not over 77 Celcius.4. At 100 Celcius, the hops is added at a boil and the liquid is quickly cooled and yeast is

added in the line.5. The yeast ferments at 20 Celcius. When the yeast is added to the wort, the fermenting

process begins, where the sugars turn into alcohol, carbon dioxide and other components .
http://en.wikipedia.org/wiki/Carbon_dioxidehttp://en.wikipedia.org/wiki/Carbon_dioxide

8/11/2019 Beer Foam

3/25

8/11/2019 Beer Foam

4/25

8/11/2019 Beer Foam

5/25



List of Figures:

Figure 1. Derek Doc Osborn ..................................................................................................................... 7

Figure 2 : Half Normal Plot ........................................................................................................................ 11

Figure 3 : Normal Plot of Residuals ............................................................................................................ 12

Figure 4:Box-Cox Plot ................................................................................................................................ 13

Figure 5: Normal Plot of Residuals for the Final Reduction Model ........................................................... 16

Figure 6: Residuals Vs Run Order .............................................................................................................. 17

Figure 7: Residuals Vs Predicted ................................................................................................................ 18

Figure 8. Plot of Residuals vs Factors ......................................................................................................... 19

Figure 9. Plots of One Factor Effect ........................................................................................................... 20

Figure 10: pressure and Biofoam Interaction .............................................................................................. 21

Figure 11: Temperature and Type of Beer Interaction ................................................................................ 22

Figure 12: Temperature and Pressure Interaction ....................................................................................... 22

Figure 13: Biofoam and Type of Beer Interaction ...................................................................................... 23

8/11/2019 Beer Foam

6/25



List of Tables:

Table 1. Beer Chemistry ............................................................................................................................... 7

Table 2: Factor Levels and Codes ................................................................................................................. 8

Table 3: Test Matrix ...................................................................................................................................... 9

Table 4: ANOVA for the Full Design ......................................................................................................... 10

Table 5: R Squared Values for Complete Design ....................................................................................... 12

Table 6: ANOVA Table without Outliers ................................................................................................... 14

Table 7. ANOVA Table without Outliers and Non-Significant Terms ...................................................... 15

Table 8. Comparison of R-Squared ............................................................................................................. 15

8/11/2019 Beer Foam

7/25



1. PROJECT STATEMENT & OBJECTIVESThe scope of the experiment is to analyze the factors affecting the amount of foam head created while

pouring a draft beer. There are cosmetic and financial impacts regarding the serving of draft beer.Excessive foam is unacceptable to the consumer and the brewer. The consumer would not wantexcessive foam since they are paying for a beer. For the brewer, excessive foam at the pour of thedraft beer may allow for a large quantity of foam, which is equivalent to 20% liquid, be wasted downthe drain as the beer foam spills over the full glass. No foam,however, does not capture the aromatic and customer standardsfor a draft beer. The factors evaluated include pressure of thedraft line, the type of beer (chemistry plays a role in foaming),the temperature of the beer in the draft line, use of a foamingagent, Biofoam CL, and a block factor of operator. BJs Breweryin Chandler, and their head brewer, De rek Doc Osborn, has

been instrumental in assisting our team with this designedexperiment. Derek wanted to determine if adding biofoam is a

cost effective means of increasing foam head of a beer under theinfluence of various factors.

2. INTRODUCTIONThe objective of the experiment is to analyze the factorsinvolved in the amount of foam head on a draft beer.Worldwide cultural traditions indicate that there are a varietyof acceptable standards based on the type of beer, the historyof beer brewing, and the customer expectations with relationship to the cost of a beer. MostAmerican draft beers have the expectation of about .5 to 1 inches (1.27 to 2.54 cm) of head tofulfill a need for cosmetic looks and aromatic release of flavor as bubbles pop over the surface ofthe beer. At BJs Brewery, the standard draft is poured at 20 psi, at a temperature of 37 to 40degrees Fahrenheit, without Biofoam CL. Our experimental design included a type of beerfactor since the chemistry of the beer will affect its ability to foam at pour. Bartenders at

breweries are trained to pour draft beers with specific guidelines. Despite training, there may bean uncontrollable variation from operator to operator that has been included is a block factor withtwo operators. The variation of pressure in this designed experiment, 11 and 24 psi, stood aboveand below the standard pour pressure of 20. The temperature levels, 37 and 58 degrees Fahrenheit,are the extremes of pouring and serving beer. Many beers are expected to warm and accentuatetheir flavors as the beer warms after the pour, especially the red beers. The two beers selected,Jeremiah Red and Lightswitch, were selected based on their chemistry. These beers elicit the

spectrum of inherent foaming capability, red being the most and lightswitch being the least.

Lights witch Jeremiah Red2 row base malt (silo) 2 row base malt (silo)Wheat Malt 4 other maltshops hopsWater WaterYeast Yeast

Table 1. Beer Chemistry

Figure 1. Derek Doc Osborn

8/11/2019 Beer Foam

8/25



The factors affecting the foaming ability in the chemistry make up of the beers is the larger quantity of 2row base barley that is double of the amount in the red beer. The malt amount by weight is four times asmuch in the red beer. The other ingredients are the same in each beer; hops, water, and yeast.

3. EXPERIMENTAL DESIGN

3.1 Design Factors and LevelIn this experiment we have several controllable fixed factors that affect the height of the beer foam. Thefactors levels and code are listed in the following table.

Factors + (High) (Low)

Keg Pressure (psi) 1 (24) -1 (11)

Temperature at Keg (F) 1 (58) -1 (37)

The use of Biofoam 1 (used) -1 (not used)

Type of Beer 1 (Red) -1 (Light)

Table 2: Factor Levels and Codes

For each factor, we have two levels associated with it. The Keg pressure has been taken into considerationfor the fact that the higher pressure you put on it the high level of CO 2 you will have in the beer whichmakes it easily released. The same concept can be applied for the temperature factor the cooler the beerthe more CO 2 we will have in it. Low pressure is assumed to create a larger variation in data due to CO 2 wanting to break out since there is no pressure to secure it. There may also be more va riation in resultswith low pressure lines due to inconsistency in the line(actual pressure data). The Biofoam product is anadditive substance that helps to increase foam head at the pour and to stabilize the foam from collapsing.The bartender (operator ) is a block to eliminate the nuisances created with this factor so we reduce itscontribution for the experimental errors.

3.2 Constant FactorsIn the experiment three factors held constant; the mug shape, the room temperature, and the bar line.

4. EXPERIMENTAL PROCEDURELooking at the factors, we have 4 fixed factors level and one nuisance factor we decided to run theexperiment as full factorial 2 4 design with two blocks representing the two operators. There will be 32runs for this designed experiment. Then we generate the randomized test matrix that reduces thevariation caused by the pattern of the experiment.

1. After setting up the experiment we adjust the factor to the desired levels. 2. Pour the beer into the mug. 3. Measure the original foam height ( after 10sec from the pour step ) (20% of the foam is beer as

per the expert background, hence a short delay in measuring ) 4. Repeat the previous steps with the next required levels.

8/11/2019 Beer Foam

9/25



5. EXPERIMENTAL MATRIXWe decided 2 4 full factorial design with 2 replicates depending on 2 blocks. Our experiment is total32 runs that were divided into 2 blockings. This model used coded value for each factor.

Table 3: Test Matrix

Response

A:Pressure C:Type ofBiofoam

D:Type ofBeer

B:Temperature

Height ofBeer Foam

psi F cm

19 1 Operator1 1 -1 -1 1 3.7

13 2 Operator1 -1 1 1 -1 1.9

21 3 Operator1 -1 1 -1 1 2.5

9 4 Operator1 -1 -1 1 -1 0.9

15 5 Operator1 1 1 1 -1 1.8

25 6 Operator1 -1 -1 1 1 3.5

3 7 Operator1 1 -1 -1 -1 1.9

11 8 Operator1 1 -1 1 -1 2.917 9 Operator1 -1 -1 -1 1 4.5

23 10 Operator1 1 1 -1 1 3.6

29 11 Operator1 -1 1 1 1 6

27 12 Operator1 1 -1 1 1 7.2

7 13 Operator1 1 1 -1 -1 3

5 14 Operator1 -1 1 -1 -1 6.8

1 15 Operator1 -1 -1 -1 -1 1

31 16 Operator1 1 1 1 1 4.6

24 17 Operator2 1 1 -1 1 5.4

2 18 Operator2 -1 -1 -1 -1 1.4

12 19 Operator2 1 -1 1 -1 6

30 20 Operator2 -1 1 1 1 5.7

14 21 Operator2 -1 1 1 -1 4.7

26 22 Operator2 -1 -1 1 1 5.1

22 23 Operator2 -1 1 -1 1 4

4 24 Operator2 1 -1 -1 -1 4

18 25 Operator2 -1 -1 -1 1 2.5

6 26 Operator2 -1 1 -1 -1 8.9

28 27 Operator2 1 -1 1 1 8.2

20 28 Operator2 1 -1 -1 1 6.4

10 29 Operator2 -1 -1 1 -1 2.5

32 30 Operator2 1 1 1 1 7

8 31 Operator2 1 1 -1 -1 4.5

16 32 Operator2 1 1 1 -1 3.2

Std Run Block

Factor

8/11/2019 Beer Foam

10/25



6. RESULTS AND ANALYSIS 6.1 Estimate Factor EffectsThe main effects and the interaction effects were calculated, and in terms of checking normalityof the model and ANOVA table, the model could be renovated by model refinement in order toobtain a better model. The half normal plot was utilized in finding the significant factors thataffect the response. The following table is the experimental matrix that was utilized in our DOE

project. This model was simulated by using Design-Expert 8.0.

6.1.1 Analysis of Variance

First of all, ANOVA (analysis of variance) table was created based on the data that were obtained by 32 tests. The table below showed that this model is significant because of p-value.

Table 4: ANOVA for the Full Design

Based on this table, the influential factors in this model are three main factors (A-pressure, B- biofoam, D-temperature) except the factor C (Type of Beer). Beside AC, ABC, and ACD, almostof interaction factors were determined as a significant. This indicated that these factors havestrong association with each other. Mostly, this model looks a strong model based on p-value. Tofind out influential factors of this model accurately, we utilized in half normal plot.

p-valueProb > F

Block 17.5528 1 17.5528

Model 107.6697 15 7.1780 8.8674 < 0.0001 significant A-Pressure 4.1328 1 4.1328 5.1055 0.0392 B-Biofoam 4.4253 1 4.4253 5.4669 0.0336

C-Type of Beer 1.5753 1 1.5753 1.9461 0.1833 D-Temperature 18.7578 1 18.7578 23.1727 0.0002

AB 21.6153 1 21.6153 26.7027 0.0001 AC 2.9403 1 2.9403 3.6324 0.0760 AD 5.3628 1 5.3628 6.6250 0.0212 BC 6.7528 1 6.7528 8.3422 0.0113 BD 8.5078 1 8.5078 10.5102 0.0055

CD 15.5403 1 15.5403 19.1979 0.0005 ABC 0.0903 1 0.0903 0.1116 0.7430 ABD 3.9903 1 3.9903 4.9295 0.0422 ACD 1.7578 1 1.7578 2.1715 0.1613 BCD 8.5078 1 8.5078 10.5102 0.0055

ABCD 3.7128 1 3.7128 4.5867 0.0490Residual 12.1422 15 0.8095Cor Total 137.3647 31

SourceSum ofSquares

DFMean

SquaresF-Value

8/11/2019 Beer Foam

11/25



6.1.2 Normal Plot Analysis 6.1.2.1 Half Normal Plot

The figure below was the half normal plot of this model.

Figure 2 : Half Normal Plot

This is the plot of the absolute value of the effect estimates against their cumulative normal

probabilities. Except ABC, one of three-factor interactions, every factor seems to be significant.

6.1.2.2 Normal Plot of Residuals

The figure below is the normal plot of residuals in this model.

Design-Expert?SoftwareHeight of Beer Foam

Error estimates A: PressureB: BiofoamC: Type of Beer D: Temperature

Positive EffectsNegative Effects

Half-Normal Plot

H a

l f - N o r m a

l %

P r o

b a

b i l i t y

|Standardized Effect|

0.00 0.41 0.82 1.23 1.64

0102030

50

70

80

90

95

99

AB

C

D

AB

AC

ADBC

BD

CD

ABC

ABD ACD

BCD

ABCD

8/11/2019 Beer Foam

12/25



Figure 3 : Normal Plot of Residuals

There are obviously two outliers (std.17 and std.18 in the table) found in this plot. Based onthe influential points from Design-Expert 8.0, these two points are turned out the outliers becausestudentized residuals and fitted value (DFFITS) of two points exceed the limits (|4.25|, |-4.25| >3.85). DFFITS is the way to measure the influence of the ith observation on the fitted value instandard deviation units. However, except those outliers found, this plot has no severe problemfor normality of the model.

6.1.3 R-Squared

Various R-Squared values are presented in the table below.

Table 5: R Squared Values for Complete Design

The R-Squared is to confirm the proportion of total variability. This model has the R-Squared of 0.8987, which is probably a good model. However, this model had significantdifference between "Adj R-Squared" of 0.7973and "Pred R-Squared" of 0.5388. This means thatthis model could have a large block effect or possibility of model or data problem. We can tryseveral ways (i.e. response transformation, model reduction, outliers, etc) to make a better model.


Color points by value of Height of Beer Foam:

8.9

0.9

Internally Studentized Residuals

N o r m a

l %

P r o

b a

b i l i t y

Normal Plot of Residuals

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00

1

5

10

20

30

50

70

80

90

95

99

Std. Dev. 0.8997 R-Squared 0.8987

Mean 4.2281 Adj R-Squared 0.7973

C.V. % 21.2792 Pred R-Squared 0.5388

8/11/2019 Beer Foam

13/25



6.1.4 Model Refinement6.1.4.1 Box-Cox Plot

For the most suitable transformation way, Box-Cox method is generally utilized. Thefigure below is the result of Box-Cox plot for this model.

Figure 4:Box-Cox Plot

Lamda calculated in box-cox method is 1, meaning there is no recommended transformationof response to make a better model. So, for this model, transformation does not work well.

6.1.5 Model Reduction: Discarding Outliers

Beside the transformation, the residual plots above indicated there are two outliers that couldaffect this model differently. There are two ways of controlling outliers. One suggestion is tosubstitute these oultiers for an estimate that is described by Chapter 4 for blocked designs(Motgomery, 2008). This will help keeping the orthogonality of the design, which makes analysiseasy. The other way is to discard an outlier and analyzing the remining observations. This couldmake our model non-orthogonal, but the least squared does not need an orthogonal design so thatthis model could be analyzed regardless of orthogonality. Also, the correlation, which affects the

normal probability plotting, is very small by a missing observation relatvely in 2k design havingat least 4 factors or over. So, the researcher considered removing these outliers. The table belowis shonw the ANOVA after deleting two outliers.


LambdaCurrent = 1Best = 0.69Low C.I. = -0.04High C.I. = 1.5

Recommend transform:None (Lambda = 1)

Lambda

L n

( R e s

i d u a

l S S )

Box-Cox Plot for Power Transforms

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

-3 -2 -1 0 1 2 3

8/11/2019 Beer Foam

14/25



Table 6: ANOVA Table without Outliers

The whole model was determined as a significant one. The significant factors found in thistable are all main factors (A, B , C ,D), 4 two-factor interactions (AB, AD, BC, CD), and onethree-factor interaction (ACD). Most factors are significant in this model. Also, like the sameanalysis from the original model, every factor is drastically interacted and influenced with eachother. The table below is shown the varied R-Squared values.

R-Squared significantly was improved after discarding the outliers. It seems that there is no problem for the big difference between Adj R-Squared and Pred R-Squared in this renovatedmodel. This means discarding outliers would be a reasonable way for improving the model of this

project. In addition, we tried to have a better R-Squared model deleting BD, ABD, and BCD,which is a non-significant term. The ANOVA table below is changed below after deleting non-significant terms.

p-valueProb > F

Block 22.0163 1 22.0163Model 106.5387 14 7.6099 18.7612 < 0.0001 significant

A-Pressure 7.8400 1 7.8400 19.3285 0.0006 B-Biofoam 8.1225 1 8.1225 20.0249 0.0005

C-Type of Beer 5.0625 1 5.0625 12.4809 0.0033 D-Temperature 2.8900 1 2.8900 7.1249 0.0183

AB 21.6225 1 21.6225 53.3074 < 0.0001 AC 0.0225 1 0.0225 0.0555 0.8172 AD 9.0000 1 9.0000 22.1883 0.0003 BC 10.24 1 10.24 25.2453628 0.0002 BD 0.49 1 0.49 1.20803005 0.2903 CD 17.2225 1 17.2225 42.459791 < 0.0001

ABC 1.3225 1 1.3225 3.26044846 0.0925 ABD 0.0025 1 0.0025 0.00616342 0.9385 ACD 5.29 1 5.29 13.0417938 0.0028 BCD 0.49 1 0.49 1.20803005 0.2903Residual 5.67866667 14 0.40561905Cor Total 134.233667 29

SourceSum ofSquares

DFMean

SquaresF-Value

8/11/2019 Beer Foam

15/25



Table 7. ANOVA Table without Outliers and Non-Significant Terms

Every term looks significant but AC, which was not discarded due to hierarchy issue. This modelwas proven as a better model because of the improved R-Squared below.

Table 8. Comparison of R-Squared

The third column informed that we have a better Adj R-Squared and Pred R-Squared rather thanonly discarding outliers (second column). Adj R-Squared increases after deleting non-significant terms(BD, ABD, and BCD). This is actually a efficient improvement because R-Squared (94.13%) is almostsame as the second column (94.94%).

p-valueProb > F

Block 22.0163 1 22.0163Model 105.6249 11 9.6023 24.7616 < 0.0001 significant

A-pressure 16.0023 1 16.0023 41.2653 < 0.0001 B-biofoam 16.5123 1 16.5123 42.5805 < 0.0001

C-type 10.9203 1 10.9203 28.1603 < 0.0001 D-temperature 2.8623 1 2.8623 7.3809 0.0147

AB 40.2003 1 40.2003 103.6652 < 0.0001 AC 0.4202 1 0.4202 1.0837 0.3124 AD 18.0903 1 18.0903 46.6497 < 0.0001 BC 20.30625 1 20.30625 52.3641431 < 0.0001 CD 32.58025 1 32.58025 84.0153586 < 0.0001

ABC 3.66025 1 3.66025 9.43876171 0.0069 ACD 11.34225 1 11.34225 29.2484926 < 0.0001Residual 6.59241667 17 0.38778922Cor Total 134.233667 29

SourceSum ofSquares

DFMean

SquaresF-Value

Model Original Discarding OutliersDiscarding Outliers +

Non-significant terms

R-Squared 0.8987 0.9494 0.9413

Adj R-Squared 0.7973 0.8988 0.9032

Pred R-Squared 0.5388 0.7676 0.8173

8/11/2019 Beer Foam

16/25



6.2 Final Model: Model Adequacy Checking6.2.1 Plot of Residuals

6.2.1.1 Normal Plot of Residuals

Figure 5: Normal Plot of Residuals for the Final Reduction Model

Without outliers, the figure shows there is no doubt of normality assumption.

Design-Expert?Software

height of foamColor points by value of height of foam:

8.9

0.9

Internally Studentized Residuals

N o r m a

l %

P r o

b a

b i l i t y

Normal Plot of Residuals

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00

1

5

10

20

30

50

70

80

90

95

99

8/11/2019 Beer Foam

17/25



6.2.1.2 Run Order

Figure 6: Residuals Vs Run Order

This plot of residuals is good for checking correlation between residuals. There is no cause toconsider this model as any violation of the independence or constant variance assumptions.

6.2.1.3 Predicted Value

The next residual model with predicted value is to check another normality of model. This plot also proved there is no violation of normaility assumptions due to constant distribution andstructureless model. However, there are two outliers found easily in this plot as well. Theseoutliers were the same one found in the ANOVA table above.

Design-Expert?Softwareheight of foam

Color points by value of height of foam:

8.9

0.9

Run Number

I n t e r n a

l l y

S t u d e n

t i z e

d R e s

i d u a

l s

Residuals vs. Run

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

1 6 11 16 21 26 31

8/11/2019 Beer Foam

18/25



Figure 7: Residuals Vs Predicted

6.2.1.4 Factors

Figures below are shown the plot of residuals with each factor.

Design-Expert?Softwareheight of foam

Color points by value of height of foam:

8.9

0.9

2

Predicted

I n t e r n a

l l y

S t u d e n

t i z e

d R e s

i d u a

l s

Residuals vs. Predicted

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

0.00 2.00 4.00 6.00 8.00 10.00

A:pressure

I n t e r n a

l l y

S t u d e n

t i z e

d R e s

i d u a

l s

Residuals vs. pressure

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

-1.00 -0.50 0.00 0.50 1.00

:.

.

B:biofoam

I n t e r n a

l l y

S t u d e n

t i z e

d R e s

i d u a

l s

Residuals vs. biofoam

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

-1.00 -0.50 0.00 0.50 1.00

8/11/2019 Beer Foam

19/25



Figure 8. Plot of Residuals vs Factors

From this plot, we know the variability of each factor with some levels. The residual plotsfrom Factor B, C, D present there is little more variability at high level. The pressure (Factor A)has higher variability at low level. However, it can be concluded that there is no huge differenceof variability at each level. At low pressure, variability is more likely due to inconsistency in

pressure in the draft line.`

6.3 Final Model: One Factor EffectsThe plots of one factor below are shown respectively.

C:type

I n t e r n a

l l y

S t u d e n

t i z e

d R e s

i d u a

l s

Residuals vs. type

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

-1.00 -0.50 0.00 0.50 1.00

:.

.

2

D:temperature

I n t e r n a

l l y

S t u d e n

t i z e

d R e s

i d u a

l s

Residuals vs. temperature

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

-1.00 -0.50 0.00 0.50 1.00

-1.00 -0.50 0.00 0.50 1.00

A: pressure

h e

i g h t o

f f o a m

0

1

2

3

4

5

6 Warning! Factor involved in multiple interactions.

One Factor :

:

: .: .: .

-1.00 -0.50 0.00 0.50 1.00

B: biofoam

h e

i g h t o

f f o a m

0

1

2

3

4

5


One Factor

8/11/2019 Beer Foam

20/25



Figure 9. Plots of One Factor Effect

This plot could explain how each factor affects the response at some levels. All the plotsdescribe the height of beer foam is high at high level of each factor, and the gradient of each lineis not fairly big. At high level (high temperature, pressure, using biofoam, and red beer) of eachfactor, we will have higher height of beer foam.

6.4 Final Model: Interaction EffectsTo check the interaction effects, two-factor interactions are only considered because three-

factor interactions have small coefficients relatively. Also, two-factor interactions are goodenough to describe how differently or significantly factors are interacted with each other. This

plot is so important for our model conclusions because the effects of interaction factors areexisting based on the ANOVA table. The first plot of interaction effect is the plot between

pressure (factor A) and biofoam (factor B), which has highest sum of squares.

-1.00 -0.50 0.00 0.50 1.00

C: type

h e

i g h t o f f o a m

0

1

2

3

4

5


One Factor :

:

: .: .: .

-1.00 -0.50 0.00 0.50 1.00

D: temperature

h e

i g h t o f f o a m

0

1

2

3

4

5


One Factor

8/11/2019 Beer Foam

21/25

8/11/2019 Beer Foam

22/25



Figure 11: Temperature and Type of Beer Interaction

This plot displays that the height of beer foam is large in red beer at high temperature.Red beer is influenced by temperature variation more than light beer. On the contrary, light beeris not much affected by temperature based on two points on the left hand of this plot. The nextfigure is the interaction plot for pressure (factor A) and temperature (factor D).

Figure 12: Temperature and Pressure Interaction

Design-Expert?SoftwareFactor Coding: Actualheight of foam

X1 = C: typeX2 = D: temperature

Actual Factors A: pressure = 0.00

B: biofoam = 0.00D- -1.00D+ 1.00

D: temperature

-1.00 -0.50 0.00 0.50 1.00

C: type

h e

i g h t o

f f o a m

0

1

2

3

4

5

6

7Warning! Term involved in ACD interaction.

Interaction


X1 = A: pressureX2 = D: temperature

Actual FactorsB: biofoam = 0.00C: type = 0.00

D- -1.00D+ 1.00

D: temperature

-1.00 -0.50 0.00 0.50 1.00

A: pressure

h e

i g h t o

f f o a m

0

1

2

3

4

5

6

7 Warning! Term involved in ACD interaction.

Interaction

8/11/2019 Beer Foam

23/25



At high pressure, there is big variation of beer foam size between temperature levels,meaning both high pressure and temperature produces large size of beer foam.

Figure 13: Biofoam and Type of Beer Interaction

This plot is the interaction plot between biofoam and type beer. Interestingly, type of beer ishighly influenced when beer has no biofoam. Without influence of biofoam, red beer produces more

beer foam than light beer. However, all types of beer make greater beer foam using biofoam. This proves that beerfoam produces more beer foam.

In summary, all main factors are significant in height of beer foam based on the ANOVAtable. However, the interaction between main factors strongly affects this model more than only onefactor effect. Also, this could be indicated by checking the size of coefficient in the next section (6.5).This conclusion resulted from the interaction plots that have been analyzed above. In short, the size of

beer foam mostly increases at high pressure irrespective of any factors. Using biofoam (factor B) also produces higher size of beer foam relatively. Furthermore, temperature severely varies depending on pressure and type of beer. Temperature itself has lowest effects for the response relatively. Red beergenerally has more foam than light beer.


X1 = B: biofoam

X2 = C: type

Actual Factors A: pressure = 0.00D: temperature = 0.00

C- -1.00C+ 1.00

C: type

-1.00 -0.50 0.00 0.50 1.00

B: biofoam

h e

i g h t o

f f o a m

0

1

2

3

4

5

6

7Warning! Term involved in ABC interaction.

Interaction

8/11/2019 Beer Foam

24/25



6.5 Final Regression ModelThe coded and actual final regression models are shown below.

Final Equation in Terms of Coded Factors:

height of foam =

+3.80+0.79 * A+0.80 * B+0.65 * C+0.33 * D-1.25 * A * B-0.13 * A * C

+0.84 * A * D-0.89 * B * C+1.13 * C * D+0.38 * A * B * C-0.67 * A * C * D

Final Equation in Terms of Actual Factors:

height of foam =+3.79688+0.79063 * pressure+0.80312 * biofoam+0.65312 * type+0.33438 * temperature-1.25312 * pressure * biofoam-0.12812 * pressure * type+0.84062 * pressure * temperature-0.89062 * biofoam * type+1.12813 * type * temperature+0.37812 * pressure * biofoam * type-0.66563 * pressure * type * temperature

As looking at the coefficients of each factor, two-factor interactions have large number except AC,indicating each factor strongly influences beer foam height when they interact.

8/11/2019 Beer Foam

25/25


7. CONCLUSIONS AND RECONMMENDATIONThe brewery has two objectives in draft beer service regarding foam height. The first is a foam that is

adequate relative the mug size the mug size and beer foam that does not dissipate too quickly as thecustomer drinks the beer. From the analysis the observations find that red beer (due to its chemicalcomposition) have more potential to create high foam (figure 18). That gives a clue to pay more attentionwhen trying to reduce the foam it produces by controlling the factors that have a significant affect.However, the presence of biofoam for red beer does not have a huge affect in the foam height. On theother hand biofoam has a significant effect in keeping high foam in light beer so the same decision will bemade for not using it. When looking at the interaction between beer type and temperature (figure 16) thetemperature affects the red beer more significantly, so in order to reduce the beer foam height, have theline in cold temperature. Also, the biofoam does not have a big affect on the foam height when handlingin high pressure. Moreover, the selection of pressure and temperature as factors affecting the processdefines an overlap with each other since both factors help to increase the level of CO 2 in the beer. WhenTo observe the interaction between these factors, look for a combination of high pressure and lowtemperature to reduce the foam height (figure 16).

Based on what Derek said about the suitable temperature for each beer type, the optimum temperature forred beer is between 37 and 40 Fahrenheit. The taste of red beer in these temperatures could be better as itwarms up depending on customer preference. This temperature range is applied to light beer as well. Thisdescription is in accord with the analysis of this experiment because the temperature chosen in thisexperiment was 39 Fahrenheit, which is placed within this range (37 to 40 Fahrenheit). Figure 16 and 17

proved low temperature created a relatively small beer foam even though light beer has more foam withlow temperature than red one.

To summarize the result of the analysis and mention some recommendations consider that this model hasvery strong interactions of each factor. To achieve adequate beer foam for customers and managers, low

pressure without biofoam is required regardless of temperature effect. In beer type, red beer producesmore foam than light beer. However, most customers prefer red beer to light. For the red one, the bestcombination would be to pour in low temperature with low pressure. Keeping low temperature intransferring beer lines could mostly be recommended for relatively smaller beer foam. Generally, biofoamis utilized depending customer preference, because some customers want more beer foam. Thus, optimalcondition to pour for beer height foam will be to control low pressure, not using biofoam, and keeping

beer lines in low temperature (37 to 40 F).

8. REFERENCES

Montgomery, C. Douglas, (2008), Design and Analysis of Experiments. , John Wiley & Sons, Inc. , 7 th edition.

http://en.wikipedia.org/wiki/Brewing .

http://www.asbcnet.org/
http://en.wikipedia.org/wiki/Brewinghttp://en.wikipedia.org/wiki/Brewinghttp://en.wikipedia.org/wiki/Brewing

beer foam

Documents