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)
IEE 572 Project
Height of Beer Foam
EXECUTIVE SUMMARY
Brewing and serving beer is a cultural and social subject in the United States. The chemistry and
quantitative subject matter is organized by the American Society of Brewing Chemists, an
organization 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, BJ’s
Brewery, to determine if an additive Biofoam CL could increase the foam head of a beer and if
so, under what conditions. BJ’s Brewery also wanted data on temperature and pressure.
The above photo is the “laboratory” for BJ’s Brewery. There are 5 major steps in the brewing
process.
1.
2.
3.
4.
Malted barley is mixed with hot water to 65 to 75 Celcius. This is called mashing.
Lautering is a filter process to remove husks left over from the grains.
Sparging is then completed. A liquid is sprinkled over the top not over 77 Celcius.
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.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
Biofoam CL is assumed to increase both the foam head at pour and the retention of foam.
Biofoam should augment the natural foam components in beer. The experiment used four factors;
the type of beer, the pressure in the draft line, the temperature, the use/nonuse of biofoam. The
experiment also included a block factor since beer is typically served by many
trained/experienced bartenders.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
Table of Contents
EXECUTIVE SUMMARY................................................................................................................... 2
Table of Contents .................................................................................................................................. 4
List of Figures: ...................................................................................................................................... 5
List of Tables: ....................................................................................................................................... 6
1.
PROJECT STATEMENT & OBJECTIVES ........................................................................................ 7
2.
INTRODUCTION ................................................................................................................................ 7
3.
EXPERIMENTAL DESIGN ................................................................................................................ 8
3.1
Design Factors and Level .............................................................................................................. 8
3.2
Constant Factors............................................................................................................................ 8
4.
EXPERIMENTAL PROCEDURE ....................................................................................................... 8
5.
EXPERIMENTAL MATRIX ............................................................................................................... 9
6.
RESULTS AND ANALYSIS ............................................................................................................. 10
6.1
Estimate Factor Effects ............................................................................................................... 10
6.2
Final Model: Model Adequacy Checking ................................................................................... 16
6.3
Final Model: One Factor Effects ................................................................................................. 19
6.4
Final Model: Interaction Effects ................................................................................................. 20
6.5
Final Regression Model .............................................................................................................. 24
7.
CONCLUSIONS AND RECONMMENDATION ............................................................................. 25
8.
REFERENCES ................................................................................................................................... 25
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Height of Beer Foam
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
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
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
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
1. PROJECT STATEMENT & OBJECTIVES
The 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 want
excessive foam since they are paying for a beer. For the brewer, excessive foam at the pour of the
draft beer may allow for a large quantity of foam, which is equivalent to 20% liquid, be wasted down
the drain as the beer foam spills over the full glass. No foam,
however, does not capture the aromatic and customer standards
for a draft beer. The factors evaluated include pressure of the
draft line, the type of beer (chemistry plays a role in foaming),
the temperature of the beer in the draft line, use of a foaming
agent, Biofoam CL, and a block factor of operator. BJ’s Brewery
in Chandler, and their head brewer, Derek “Doc” Osborn, has
been instrumental in assisting our team with this designed
experiment. Derek wanted to determine if adding biofoam is a
cost effective means of increasing foam head of a beer under the
influence of various factors.
2. INTRODUCTION
The objective of the experiment is to analyze the factors
involved in the amount of foam head on a draft beer.
Figure 1. Derek “Doc” Osborn
Worldwide cultural traditions indicate that there are a variety
of acceptable standards based on the type of beer, the history
of beer brewing, and the customer expectations with relationship to the cost of a beer. Most
American draft beers have the expectation of about .5 to 1 inches (1.27 to 2.54 cm) of head to
fulfill a need for cosmetic looks and aromatic release of flavor as bubbles pop over the surface of
the beer. At BJ’s Brewery, the standard draft is poured at 20 psi, at a temperature of 37 to 40
degrees Fahrenheit, without Biofoam CL. Our experimental design included a “type” of beer
factor 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 be
an uncontrollable variation from operator to operator that has been included is a block factor with
two operators. The variation of pressure in this designed experiment, 11 and 24 psi, stood above
and 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 accentuate
their 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
2 row base malt (silo)
Wheat Malt
hops
Water
Yeast
Jeremiah Red
2 row base malt (silo)
4 other malts
hops
Water
Yeast
Table 1. Beer Chemistry
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
The factors affecting the foaming ability in the chemistry make up of the beers is the larger quantity of 2
row base barley that is double of the amount in the red beer. The malt amount by weight is four times as
much 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 Level
In this experiment we have several controllable fixed factors that affect the height of the beer foam. The
factors 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 consideration
for the fact that the higher pressure you put on it the high level of CO2 you will have in the beer which
makes it easily released. The same concept can be applied for the temperature factor the cooler the beer
the more CO2 we will have in it. Low pressure is assumed to create a larger variation in data due to CO2
wanting to “break out” since there is no pressure to secure it. There may also be more variation in results
with low pressure lines due to inconsistency in the line(actual pressure data). The Biofoam product is an
additive 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 its
contribution for the experimental errors.
3.2 Constant Factors
In the experiment three factors held constant; the mug shape, the room temperature, and the bar line.
4. EXPERIMENTAL PROCEDURE
Looking at the factors, we have 4 fixed factors level and one nuisance factor we decided to run the
experiment as full factorial 24 design with two blocks representing the two operators. There will be 32
runs for this designed experiment. Then we generate the randomized test matrix that reduces the
variation 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.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
5. EXPERIMENTAL MATRIX
We decided 24 full factorial design with 2 replicates depending on 2 blocks. Our experiment is total
32 runs that were divided into 2 blockings. This model used coded value for each factor.
Std
Run
Block
A:Pressure
psi
Factor
Response
C:Type of D:Type of B:Temperat Height of
Biofoam
Beer
ure
Beer Foam
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
2.9
17
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
Table 3: Test Matrix
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
6. RESULTS AND ANALYSIS
6.1 Estimate Factor Effects
The main effects and the interaction effects were calculated, and in terms of checking normality
of the model and ANOVA table, the model could be renovated by model refinement in order to
obtain a better model. The half normal plot was utilized in finding the significant factors that
affect 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.
Source
Block
Model
A-Pressure
B-Biofoam
C-Type of Beer
D-Temperature
AB
AC
AD
BC
BD
CD
ABC
ABD
ACD
BCD
ABCD
Residual
Cor Total
Sum of
Squares
17.5528
107.6697
4.1328
4.4253
1.5753
18.7578
21.6153
2.9403
5.3628
6.7528
8.5078
15.5403
0.0903
3.9903
1.7578
8.5078
3.7128
12.1422
137.3647
DF
1
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
31
Mean
Squares
17.5528
7.1780
4.1328
4.4253
1.5753
18.7578
21.6153
2.9403
5.3628
6.7528
8.5078
15.5403
0.0903
3.9903
1.7578
8.5078
3.7128
0.8095
F-Value
p-value
Prob > F
8.8674
5.1055
5.4669
1.9461
23.1727
26.7027
3.6324
6.6250
8.3422
10.5102
19.1979
0.1116
4.9295
2.1715
10.5102
4.5867
< 0.0001
0.0392
0.0336
0.1833
0.0002
0.0001
0.0760
0.0212
0.0113
0.0055
0.0005
0.7430
0.0422
0.1613
0.0055
0.0490
significant
Table 4: ANOVA for the Full Design
Based on this table, the influential factors in this model are three main factors (A-pressure, Bbiofoam, D-temperature) except the factor C (Type of Beer). Beside AC, ABC, and ACD, almost
of interaction factors were determined as a significant. This indicated that these factors have
strong association with each other. Mostly, this model looks a strong model based on p-value. To
find out influential factors of this model accurately, we utilized in half normal plot.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
6.1.2
Height of Beer Foam
Normal Plot Analysis
6.1.2.1 Half Normal Plot
The figure below was the half normal plot of this model.
Design-Expert?Software
Height of Beer Foam
Half-Normal Plot
99
H a lf-N o rm a l % P ro b a b ility
Error estimates
A: Pressure
B: Biofoam
C: Type of Beer
D: Temperature
Positive Effects
Negative Effects
AB
95
D
CD
90
80
AD
B
A
ABD
ACABCD
CACD
70
50
30
20
10
0
BC
BCD
BD
ABC
0.00
0.41
0.82
1.23
1.64
|Standardized Effect|
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.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
Design-Expert?Software
Height of Beer Foam
Normal Plot of Residuals
Color points by value of
Height of Beer Foam:
8.9
99
N o rm a l % P ro b a b ility
0.9
95
90
80
70
50
30
20
10
5
1
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Internally Studentized Residuals
Figure 3 : Normal Plot of Residuals
There are obviously two outliers (std.17 and std.18 in the table) found in this plot. Based on
the influential points from Design-Expert 8.0, these two points are turned out the outliers because
studentized 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 in
standard deviation units. However, except those outliers found, this plot has no severe problem
for normality of the model.
6.1.3
R-Squared
Various R-Squared values are presented in the table below.
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
Table 5: R Squared Values for Complete Design
The “R-Squared” is to confirm the proportion of total variability. This model has the RSquared of 0.8987, which is probably a good model. However, this model had significant
difference between "Adj R-Squared" of 0.7973and "Pred R-Squared" of 0.5388. This means that
this model could have a large block effect or possibility of model or data problem. We can try
several ways (i.e. response transformation, model reduction, outliers, etc) to make a better model.
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IEE 572 Project
6.1.4
Height of Beer Foam
Model Refinement
6.1.4.1 Box-Cox Plot
For the most suitable transformation way, Box-Cox method is generally utilized. The
figure below is the result of Box-Cox plot for this model.
Design-Expert?Software
Height of Beer Foam
Box-Cox Plot for Power Transforms
Lambda
Current = 1
Best = 0.69
Low C.I. = -0.04
High C.I. = 1.5
9.00
L n (R e s id u a lS S )
8.00
Recommend transform:
None
(Lambda = 1)
7.00
6.00
5.00
4.00
3.00
2.00
-3
-2
-1
0
1
2
3
Lambda
Figure 4:Box-Cox Plot
Lamda calculated in box-cox method is 1, meaning there is no recommended transformation
of 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 could
affect this model differently. There are two ways of controlling outliers. One suggestion is to
substitute 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 analysis
easy. The other way is to discard an outlier and analyzing the remining observations. This could
make our model non-orthogonal, but the least squared does not need an orthogonal design so that
this 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 having
at least 4 factors or over. So, the researcher considered removing these outliers. The table below
is shonw the ANOVA after deleting two outliers.
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IEE 572 Project
Height of Beer Foam
Sum of
Squares
Block
22.0163
Model
106.5387
A-Pressure
7.8400
B-Biofoam
8.1225
C-Type of Beer 5.0625
D-Temperature
2.8900
AB
21.6225
AC
0.0225
AD
9.0000
BC
10.24
BD
0.49
CD
17.2225
ABC
1.3225
ABD
0.0025
ACD
5.29
BCD
0.49
Residual
5.67866667
Cor Total
134.233667
Source
DF
1
14
1
1
1
1
1
1
1
1
1
1
1
1
1
1
14
29
Mean
Squares
22.0163
7.6099
7.8400
8.1225
5.0625
2.8900
21.6225
0.0225
9.0000
10.24
0.49
17.2225
1.3225
0.0025
5.29
0.49
0.40561905
F-Value
p-value
Prob > F
18.7612
19.3285
20.0249
12.4809
7.1249
53.3074
0.0555
22.1883
25.2453628
1.20803005
42.459791
3.26044846
0.00616342
13.0417938
1.20803005
< 0.0001
0.0006
0.0005
0.0033
0.0183
< 0.0001
0.8172
0.0003
0.0002
0.2903
< 0.0001
0.0925
0.9385
0.0028
0.2903
significant
Table 6: ANOVA Table without Outliers
The whole model was determined as a significant one. The significant factors found in this
table are all main factors (A, B , C ,D), 4 two-factor interactions (AB, AD, BC, CD), and one
three-factor interaction (ACD). Most factors are significant in this model. Also, like the same
analysis from the original model, every factor is drastically interacted and influenced with each
other. 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 renovated
model. 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 nonsignificant terms.
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IEE 572 Project
Height of Beer Foam
Sum of
Squares
Block
22.0163
Model
105.6249
A-pressure
16.0023
B-biofoam
16.5123
C-type
10.9203
D-temperature
2.8623
AB
40.2003
AC
0.4202
AD
18.0903
BC
20.30625
CD
32.58025
ABC
3.66025
ACD
11.34225
Residual
6.59241667
Cor Total
134.233667
Source
DF
1
11
1
1
1
1
1
1
1
1
1
1
1
17
29
Mean
Squares
22.0163
9.6023
16.0023
16.5123
10.9203
2.8623
40.2003
0.4202
18.0903
20.30625
32.58025
3.66025
11.34225
0.38778922
F-Value
p-value
Prob > F
24.7616
41.2653
42.5805
28.1603
7.3809
103.6652
1.0837
46.6497
52.3641431
84.0153586
9.43876171
29.2484926
< 0.0001
< 0.0001
< 0.0001
< 0.0001
0.0147
< 0.0001
0.3124
< 0.0001
< 0.0001
< 0.0001
0.0069
< 0.0001
significant
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 model
was proven as a better model because of the improved R-Squared below.
Model
Original
Discarding Outliers
Discarding 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
Table 8. Comparison of R-Squared
The third column informed that we have a better Adj R-Squared and Pred R-Squared rather than
only 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 almost
same as the second column (94.94%).
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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Height of Beer Foam
6.2 Final Model: Model Adequacy Checking
6.2.1 Plot of Residuals
6.2.1.1 Normal Plot of Residuals
Design-Expert?Software
height of foam
Normal Plot of Residuals
Color points by value of
height of foam:
8.9
99
N o rm a l % P ro b a b ility
0.9
95
90
80
70
50
30
20
10
5
1
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
Internally Studentized Residuals
Figure 5: Normal Plot of Residuals for the Final Reduction Model
Without outliers, the figure shows there is no doubt of normality assumption.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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Height of Beer Foam
6.2.1.2 Run Order
Design-Expert?Software
height of foam
0.9
3.00
In te rn a lly S tu d e n tiz e d R e s id u a ls
Color points by value of
height of foam:
8.9
Residuals vs. Run
2.00
1.00
0.00
-1.00
-2.00
-3.00
1
6
11
16
21
26
31
Run Number
Figure 6: Residuals Vs Run Order
This plot of residuals is good for checking correlation between residuals. There is no cause to
consider 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 and
structureless model. However, there are two outliers found easily in this plot as well. These
outliers were the same one found in the ANOVA table above.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
Design-Expert?Software
height of foam
Residuals vs. Predicted
Color points by value of
height of foam:
8.9
In te rn a lly S tu d e n tiz e d R e s id u a ls
3.00
0.9
2.00
1.00
0.00
-1.00
2
-2.00
-3.00
0.00
2.00
4.00
6.00
8.00
10.00
Predicted
Figure 7: Residuals Vs Predicted
6.2.1.4 Factors
Figures below are shown the plot of residuals with each factor.
Design-Expert?Software
xpert?Software
foam
Residuals vs. biofoam
of foam
Residuals vs.height
pressure
Color points by value of
height of foam:
8.9
In te rn a lly S tu d e n tiz e d R e s id u a ls
3.00
3.00
In te rn a lly S tu d e n tiz e d R e s id u a ls
nts by value of
foam:
0.9
2.00
1.00
0.00
-1.00
-2.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
-3.00
-1.00
-0.50
0.00
0.50
A:pressure
Serhan Alshammari, Jinsung Cho, Tracy Lenz
1.00
-1.00
-0.50
0.00
0.50
1.00
B:biofoam
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Height of Beer Foam
xpert?Software
foam
Design-Expert?Software
Residuals vs.
heighttype
of foam
In te rn a lly S tu d e n tiz e d R e s id u a ls
Residuals vs. temperature
Color points by value of
height of foam:
8.9
3.00
3.00
In te rn a lly S tu d e n tiz e d R e s id u a ls
nts by value of
foam:
0.9
2.00
1.00
0.00
-1.00
-2.00
2.00
1.00
0.00
-1.00
2
-2.00
-3.00
-3.00
-1.00
-0.50
0.00
0.50
-1.00
1.00
-0.50
0.00
0.50
1.00
D:temperature
C:type
Figure 8. Plot of Residuals vs Factors
From this plot, we know the variability of each factor with some levels. The residual plots
from 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 difference
of 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 Effects
The plots of one factor below are shown respectively.
Expert?Software
oding: Actual
foam
Design-Expert?Software
One Factor
Factor Coding: Actual
One Factor
height of foam
Warning! Factor involved in multiple interactions.
6
ressure
actors
m = 0.00
0.00
rature = 0.00
X1 = B: biofoam
Actual Factors
A: pressure = 0.00
C: type = 0.00
D: temperature = 0.00
5
h e ig h t o f fo a m
h e ig h t o f fo a m
5
4
3
2
4
3
2
1
1
0
0
-1.00
-0.50
0.00
0.50
A: pressure
Serhan Alshammari, Jinsung Cho, Tracy Lenz
Warning! Factor involved in multiple interactions.
6
1.00
-1.00
-0.50
0.00
0.50
1.00
B: biofoam
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IEE 572 Project
Expert?Software
oding: Actual
foam
Height of Beer Foam
Design-Expert?Software
One Factor
Factor Coding: Actual
One Factor
height of foam
Warning! Factor involved in multiple interactions.
6
ype
X1 = D: temperature
actors
ure = 0.00
m = 0.00
rature = 0.00
Actual Factors
A: pressure = 0.00
B: biofoam = 0.00
C: type = 0.00
5
h e ig h t o f fo a m
h e ig h t o f fo a m
5
Warning! Factor involved in multiple interactions.
6
4
3
2
1
4
3
2
1
0
0
-1.00
-0.50
0.00
0.50
1.00
-1.00
C: type
-0.50
0.00
0.50
1.00
D: temperature
Figure 9. Plots of One Factor Effect
This plot could explain how each factor affects the response at some levels. All the plots
describe the height of beer foam is high at high level of each factor, and the gradient of each line
is not fairly big. At high level (high temperature, pressure, using biofoam, and red beer) of each
factor, we will have higher height of beer foam.
6.4 Final Model: Interaction Effects
To check the interaction effects, two-factor interactions are only considered because threefactor interactions have small coefficients relatively. Also, two-factor interactions are good
enough 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 are
existing 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.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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IEE 572 Project
Height of Beer Foam
Design-Expert?Software
Factor Coding: Actual
height of foam
Interaction
Warning! Term involved in ABC interaction.
6
Actual Factors
C: type = 0.00
D: temperature = 0.00
5
h e ig h t o f fo a m
B- -1.00
B+ 1.00
B: biofoam
7
X1 = A: pressure
X2 = B: biofoam
4
3
2
1
0
-1.00
-0.50
0.00
0.50
1.00
A: pressure
Figure 10: pressure and Biofoam Interaction
On the left hand side of this plot, two points represent levels of biofoam (factor B) at low
pressure without any influence of the other factors (type of beer, temperature). This means
biofoam affects the height of foam at low pressure. At low pressure, the existence of biofoam will
highly multiply the size of beer foam. On the contrary, the size of beer foam is high at high
pressure regardless of the existence of biofoam. The next figure is the interaction plot between
type of beer (factor C) and temperature (factor D), which has the second highest sum of squares.
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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Height of Beer Foam
Design-Expert?Software
Factor Coding: Actual
height of foam
Interaction
Warning! Term involved in ACD interaction.
6
Actual Factors
A: pressure = 0.00
B: biofoam = 0.00
5
h e ig h t o f fo a m
D- -1.00
D+ 1.00
D: temperature
7
X1 = C: type
X2 = D: temperature
4
3
2
1
0
-1.00
-0.50
0.00
0.50
1.00
C: type
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 beer
is not much affected by temperature based on two points on the left hand of this plot. The next
figure is the interaction plot for pressure (factor A) and temperature (factor D).
Design-Expert?Software
Factor Coding: Actual
height of foam
Interaction
Warning! Term involved in ACD interaction.
6
Actual Factors
B: biofoam = 0.00
C: type = 0.00
5
h e ig h t o f fo a m
D- -1.00
D+ 1.00
D: temperature
7
X1 = A: pressure
X2 = D: temperature
4
3
2
1
0
-1.00
-0.50
0.00
0.50
1.00
A: pressure
Figure 12: Temperature and Pressure Interaction
Serhan Alshammari, Jinsung Cho, Tracy Lenz
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Height of Beer Foam
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.
Design-Expert?Software
Factor Coding: Actual
height of foam
Interaction
Warning! Term involved in ABC interaction.
6
Actual Factors
A: pressure = 0.00
D: temperature = 0.00
5
h e ig h t o f fo a m
C- -1.00
C+ 1.00
C: type
7
X1 = B: biofoam
X2 = C: type
4
3
2
1
0
-1.00
-0.50
0.00
0.50
1.00
B: biofoam
Figure 13: Biofoam and Type of Beer Interaction
This plot is the interaction plot between biofoam and type beer. Interestingly, type of beer is
highly 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 ANOVA
table. However, the interaction between main factors strongly affects this model more than only one
factor 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 beer
generally has more foam than light beer.
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Height of Beer Foam
6.5 Final Regression Model
The coded and actual final regression models are shown below.
Final Equation in Terms of Coded Factors:
height of foam =
+3.80
+0.79
+0.80
+0.65
+0.33
-1.25
-0.13
+0.84
-0.89
+1.13
+0.38
-0.67
*A
*B
*C
*D
*A*B
*A*C
*A*D
*B*C
*C*D
*A*B*C
*A*C*D
Final Equation in Terms of Actual Factors:
height of foam =
+3.79688
+0.79063
+0.80312
+0.65312
+0.33438
-1.25312
-0.12812
+0.84062
-0.89062
+1.12813
+0.37812
-0.66563
* pressure
* biofoam
* type
* temperature
* pressure * biofoam
* pressure * type
* pressure * temperature
* biofoam * type
* type * temperature
* pressure * biofoam * type
* 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.
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Height of Beer Foam
7. CONCLUSIONS AND RECONMMENDATION
The 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 the
customer drinks the beer. From the analysis the observations find that red beer (due to its chemical
composition) have more potential to create high foam (figure 18). That gives a clue to pay more attention
when 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 the
other hand biofoam has a significant effect in keeping high foam in light beer so the same decision will be
made for not using it. When looking at the interaction between beer type and temperature (figure 16) the
temperature affects the red beer more significantly, so in order to reduce the beer foam height, have the
line in cold temperature. Also, the biofoam does not have a big affect on the foam height when handling
in high pressure. Moreover, the selection of pressure and temperature as factors affecting the process
defines an overlap with each other since both factors help to increase the level of CO2 in the beer. When
To observe the interaction between these factors, look for a combination of high pressure and low
temperature to reduce the foam height (figure 16).
Based on what Derek said about the suitable temperature for each beer type, the optimum temperature for
red beer is between 37 and 40 Fahrenheit. The taste of red beer in these temperatures could be better as it
warms up depending on customer preference. This temperature range is applied to light beer as well. This
description is in accord with the analysis of this experiment because the temperature chosen in this
experiment 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 with
low temperature than red one.
To summarize the result of the analysis and mention some recommendations consider that this model has
very 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 produces
more foam than light beer. However, most customers prefer red beer to light. For the red one, the best
combination would be to pour in low temperature with low pressure. Keeping low temperature in
transferring beer lines could mostly be recommended for relatively smaller beer foam. Generally, biofoam
is utilized depending customer preference, because some customers want more beer foam. Thus, optimal
condition 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., 7th
edition.
http://en.wikipedia.org/wiki/Brewing.
http://www.asbcnet.org/
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