DOE Analysis of Coffee
Temperature
By: Jenny Demeules & Elliot Hagerl
5/8/15
ISyE 575
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Contents
Executive Summary ................................................................................................................. 3
Introduction .............................................................................................................................. 4
Methodology............................................................................................................................. 5
Execution.................................................................................................................................. 6
Summary of Experimental Data .............................................................................................. 8
Analysis of Results .................................................................................................................. 9
Confirmation Runs ..................................................................................................................12
Recommendations ..................................................................................................................13
Conclusions ............................................................................................................................13
Lessons Learned ....................................................................................................................13
Appendix .................................................................................................................................15
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Executive Summary
Over the past couple decades, Design of Experiments (DOE) has been one of the most
effective techniques and tools for improving processes quality throughout many industries.
Industrial engineers use DOEs in industry to perform analyses of input factors that possibly
affect the output or response of a process. These experiments can identify significant
interactions among different factors when the factors are closely examined in a controlled
environment by following a detailed procedure. Investigation of these interactions and
responses reveal conclusions that can be made to help improve the performance of an existing
process, lead to better designs that give a product a competitive edge within its field or provide
students with the most effective factors that will keep their coffee warm many hours after it is
brewed.
Inspired by the struggle to keep coffee warm, this experiment is designed to test various
factors that may affect coffee from staying warm all day long. The factors being tested in this
experiment are the type of container used (a hydroflask and thermos), the type of brewing
method used (french press or drip pot coffee maker), the addition of cream (cream or no cream
added) and finally the addition of sugar (sugar or no sugar added). This makes the experiment a
24 design without any replication conducted as a full run with 16 results. Over the course of a
weekend, these runs were carried out in accordance to a randomized run order produced in
Minitab.
After all the runs were conducted, the temperature after was reported in the response
column of Minitab and the results were analyzed. In the initial run of the experiment there was
one value well below the other values. At first this run was removed as an outlier, however,
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consultation suggested this run be repeated. The run was repeated and a more accurate result
was achieved. The interaction plots for these three Minitab results are available in the appendix
and further explain in the Summary of Experimental Data and Analysis of Results sections of
this document. The recommendations as a result of this DOE are based on the results from the
repeated outlier experiment. Concluding this experiment, the results recommend using a hydro
flask, drip pot brewing method and no cream or sugar added to the coffee. Using the procedure
identified below one should be able to produce similar results. The results of this experiment
were confirmed with 4 confirmation runs further validating the adequacy of this model and
procedure.
Introduction
Industrial Engineering students Jenny Demeules and Elliot Hagerl learned about DOE in
their ISyE course Introduction to Quality Engineering. The students then applied this knowledge
of DOE methodologies to a DOE experiment of their own. The experiment required a 24
factorial design that was unbiased, specific, measurable and practical. The students choose to
study the interaction of coffee temperature after two hours with variables of the type of
container used, the method for brewing, the addition of creamer and the addition of sugar. The
purpose of this experiment is to identify the best factors to keep coffee a reasonable
temperature for drinking all day long. While the experiment was only run for two hours, we
would assume the factors yielding the highest temperature would be consistent with a longer
period of time run. However, the constraints of time for running a full factorial design with 16
runs makes it difficult to run to observe the effects of a greater time period in this experiment.
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Methodology
This experiment is designed to measure the temperature of coffee two hours after the
substance has been brewed, measured and poured into the container. This experiment was
chosen to identify the factors that affect the temperature of coffee a couple of hours after it is
poured. The factors identified are ones that were common to the making of coffee and carrying
it around campus. Since the yield of which methods proved the best to keep coffee the
warmest, temperature was the decided response type. In this experiment no assumptions were
made and the experiment was conducted without any bias from brewing, container brands or
favorite additives to coffee, since the best method to produce the hottest coffee after 2 hours
is desired.
The runs will be conducted in the order of the random run order produced in Minitab.
Each trial will require a new pot or brew of coffee to ensure each run is independent of each
other. Once the coffee is brewed it shall be poured into the assigned container and additional
ingredients applied as necessary, a timer will begin the moment the cap of the container is
firmly sealed. The various two-level factors that will be examined throughout this trial include:
A. Storage container: Coffee will be poured into two different container types in order to
determine if storage material has any effect on the decreasing temperature rate. A
hydro flask is typically is used for keeping substances cold or hot for a long duration
while thermos are known to keep hot substances warm for long period of time.
Although both these containers incorporate a vacuum seal for insulation, there are
slight differences in the volume of these factors. Any nuisance variables such as volume
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and surface area of the containers has been minimized by using containers with similar
volume amounts and similar shapes. The low level of this factor will be specified as a
hydro flask (-1) while the high level will be a thermo (+1).
B. Brewing type: There are many different techniques used to brew coffee. However, a
Drip Pot and French Press were chosen since the students had these readily available.
The design of this experiment will have a French press (-1) set as the low variable for
this factor while a drip pot (+1) will be set as the high level.
C. Creamer: The addition of cream will also be observed in its interaction with the resulting
temperature of coffee. Creamer will be refrigerated at 45o F and immediately stirred
into the coffee after it is brewed. In this experiment coffee that receives creamer (-1)
will be considered as the low setting, while the high level of this factor will be coffee
without any cream (+1).
D. Sugar: The last factor that will be investigated in this experiment will be the addition of
sugar to coffee after it has been initially brewed. The effects of dissolvable molecule
such as sugar will be observed in respect to temperature after the set period of time.
For this experiment, sugar that is added (-1) to coffee will be low level of this variable,
while coffee without any sugar (+1) will be the high setting.
Execution
This experiment was conducted over the course of a few days in late April
approximately between the hours of 12 pm – 6 pm when the ambient temperature was most
consistent. A procedure was created to carry out this experiment. The procedure will help to
negate any nuisance variables by keeping as many variables outside of the factors being
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observed from affecting the results of this experiment. The results have been summarized in
Table 1 below.
Procedure:
The experiment is to be conducted in an environment with an ambient temperature of
68o F. The runs shall be conducted in order of the randomized run order produced in Minitab.
This will ensure the procedure is random and independent. At the start of each run, the coffee
must be brewed either in the drip pot or in the french press with only one run being brewed at
a time. This means that 18 ounces will be brewed for each trial and ¼ cup of coffee grounds
used for each run. Brewing one pot at a time will ensure that each run is independent. If the
coffee is being brewed using the french press, water must be heated to 175 o F (measured using
a thermometer) first, then poured into the press where it sits for 4 minutes to brew and then
pressed. After either type of brewing method is done, 14 ounces must be measured out using a
liquid measuring cup then poured into the respective container for measuring. Following the
pour into the container, the cream and sugar shall be added if applicable. A with cream added
shall have 2 creamer packets from McDonald’s added and one raw sugar packet from Panera
added for runs with sugar added. Note that the cream shall be in the fridge at 45 o F until the
run is started; the sugar shall be held at ambient temperature of 68o F. The lid shall be placed
on the container, then put in a closed area such as a cabinet where it will not be exposed to any
windows that could alter the surrounding temperature. Set a timer for 1 hour 58 minutes to
ensure the temperature is taken at 2 hour time period. At the 2 hour mark, the temperature
shall be taken using a digital thermometer to one decimal place and recorded on the results
column of Minitab. After the run is conducted, the container must be cleaned out with soap
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and cold water. The cold water will help lower the internal material temperature of each
container to room temperature. The thermometer shall be held half-way down and the
temperature recorded after a 30 second interval when the reading levels out. The container
must also sit for an hour following the run to further negate this variable. This process shall be
carried out until all 16 trials are completed.
Summary of Experimental Data
Below, Table 1 displays the setup of this design in Minitab. The standard order, run
order, center point, blocks, followed by factors: container, brewing type, creamer and sugar
(respectively), and finally response are stated below in the columns with the factors for each
run identified in each row. For reference the low and high values for each factor are stated
below.
Factor
Letter
Low (-1)
High (+1)
Container Type
A
Hydro
Thermo
Brew Type
B
French Press
Drip Pot
Cream
C
Creamer
No Creamer
Sugar
D
Sugar
No Sugar
Table 1: Minitab Experimental Design by Randomized Run Order
Std
Order
10
11
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Run
Order
1
2
Center
Pt
Block
s
Contain
er
Brewing Type
Creamer
Sugar
Respons
e
1
1
Thermo
French Press
Creamer
No
Sugar
122.4
Creamer
No
Sugar
130.6
1
1
Hydro
Drip Pot
1
12
3
4
1
1
1
1
Hydro
Thermo
French Press
Creamer
Sugar
127.9
Drip Pot
Creamer
No
Sugar
128.9
No
Sugar
124.8
14
5
1
1
Thermo
French Press
No
Creamer
15
6
1
1
Hydro
Drip Pot
No
Creamer
No
Sugar
134.6
6
7
1
1
Thermo
French Press
No
Creamer
Sugar
127.1
Drip Pot
No
Creamer
Sugar
131.8
Sugar
127
8
8
1
1
Thermo
5
9
1
1
Hydro
French Press
No
Creamer
7
10
1
1
Hydro
Drip Pot
No
Creamer
Sugar
131.1
16
11
1
1
Thermo
Drip Pot
No
Creamer
No
Sugar
132.4
2
12
1
1
Thermo
French Press
Creamer
Sugar
124.6
3
13
1
1
Hydro
Drip Pot
Creamer
Sugar
131.6
No
Sugar
126.2
13
14
1
1
Hydro
French Press
No
Creamer
4
15
1
1
Thermo
Drip Pot
Creamer
Sugar
130
Creamer
No
Sugar
115.3
9
16
1
1
Hydro
French Press
Analysis of Results
Analysis of the response column of Table 1 was performed at the conclusion of the 16
runs. Due to time constraints, replication of this experiment was not performed. Since there
was no replication the residual error did not receive any degrees of freedom in the ANOVA
table created in Minitab. The created ANOVA table examined the main effect interactions along
with 2-way interactions among factors. The 3rd and 4th order interactions were determined to
be insignificant these then became a part of the residual error. In total, 5 degrees of freedom
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were used for the residual error. The Normal Plot of Standardized Effects for interactions no
higher than 2nd order showed that the only significant effect was factor B, the brewing
method. The graph of this Normal Plot of Standardized Effects is available in Appendix A. This
was not a surprise as the brewing type had noticeable differences in the response when
comparing the drip runs to the press runs. The variability of this can be seen in potential
differences of the initial temperature of coffee from either of these brew methods.
However, analysis of the results showed run 16 (by the run order) as an outlier. This was
identified by the temperature of this run being noticeably lower than the rest of the responses
record for the other 15 runs. This response value was removed from Minitab and replace with
an asterisk. The analysis of factors without the outlier returned different results as the normal
plot of standardized effects identified the two factors, A- container type and C-creamer, that
were significant in addition to B, the brew method (Appendix A). It was surprising to see that
the two different types of containers as a source of variability since both of them incorporate a
similar vacuum seal design. Furthermore, multiple 2nd order interactions between factors
showed potential interaction but not enough to be deemed significant.
The adequacy of this model was assessed in Minitab by generating residual plots
(Appendix B). The normal probability plot shows all points on the graph appear to follow a
linear pattern that surround the line of best fit without any outliers. In addition, the histogram
plot resembles a bell-curve shape with the frequency at the mean being the highest bar and
increases/decreases with the respect to the residual in the respective direction. The
combination the normal probability plot and the histogram are sufficient evidence to support
the assumption that this model has normal distribution throughout. The versus fits graph show
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randomness and no obvious patterns such as fanning out are seen, making the assumption of
equal variance in this experiment. Lastly, the versus order graph does not necessarily represent
any abnormal patterns, but there does appear to be a small sequence of runs that are
consecutively decreasing. It is unclear if the assumption of independence among sampling is
supported by this final graph, with consecutive decreasing runs. However, it can be assumed
that this model has a sufficient level of adequacy for this experiment.
Furthermore, this model was used to create main effect plots, interaction plots, and a
cube plot. These plots were used to determine which factors significant in maximizing the
response of our experiment in achieving the greatest temperature response. The optimal
response for a greater temperature yield includes setting factor A to -1 (hydro flask), factor B to
+1 (drip pot), and factor C to +1 (no creamer). Although factor D was deemed insignificant, this
factor should be set to -1 (sugar) in accordance to the coefficient values generated by Minitab.
Minitab generated the significance level of .05 with the following significant factor coefficients:
Y =(x1)+(x2) + (x3)
Even though removal of the outlier proved to be an adequate model, it was suggested
that the outlier run be redone. The results from Minitab using this new value proved different
results from the previous analyses. In this model only first order and second order interactions
were observed to follow the same analysis as previously stated for the residual plots. The
normal plot of standardized effects revealed factors A, B, C and BD as significant (Appendix C).
Furthermore, the residual plots showed promising results. The normal probability plot followed
a linear relationship and histogram had a bell-curve shape. However, the histogram plot did
have a left skew. The versus fit graph appeared random with no fanning out. Additionally, the
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versus order fit showed random increases and decreases among observation order minus the 5
values that it consistently decreased. These plots make this model a valid assumption.
Using this model, Minitab generated the main effects plots, interaction plots, and cube
plots (Appendix E). This model recommends using a hydro flask, drip pot brew method, no
creamer and no sugar for the greatest yield in respect to temperature for this experiment. The
following equation using a significance of .05 gives the coefficients for the reported significant
factors.
Y=128.512-.7625(x1)+2.8625(x2)+.9625(x3)+.625(x2x4)
This model was deemed the most appropriate of all models analyzed since it included all
16 runs and there were no values identified as outliers. Confirmation of this model was done
through 2 different confirmation models each run twice for a total of 4 confirmation runs. A
prediction interval was created in Minitab (Appendix D) to compare the confirmation run values
to the model.
Confirmation Runs
The confirmation runs performed correlate to run order 6 and run order 12 respectively.
The results of the confirmation are shown below and the average of each trial taken. The
results from this table conclude that the confirmation runs are within the prediction intervals
95% confidence interval outputted by Minitab.
Run
Container
Brew
Creamer
Sugar
Result
Result Avg
1
-1
1
1
1
134.0
133.35
2
-1
1
1
1
132.7
3
1
-1
-1
-1
125.3
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125.65
4
1
-1
-1
-1
126.0
Recommendations
The results of this experiment conclude that the container, brew method and creamer
are significant factors when the highest coffee temperature after 2 hours is desired. To obtain
the “hottest” coffee after 2 hours using the factors considered and evaluated in this
experiment, one shall brew coffee using a drip pot and use a hydro flask container over a
thermos. Cream and sugar should not be added since they were shown to reduce the
temperature slightly. Using these methods, one shall be able to keep his or her coffee the
warmest throughout the day.
Conclusions
The results of this experiment show that 3 of the 4 factors were first order significant,
with the fourth factor showing significance in a second order interaction. This concludes that all
factors had an impact on the resulting temperature of coffee after a 2 hour period. This
experiment was then confirmed for validity using various residual plots generated in Minitab
and further confirmed by 4 confirmation runs well within the confidence interval specified in
Minitab. Additionally, this experiment can be replicated by someone else by following the
procedure stated above which was confirmed in 4 trail runs.
Lessons Learned
By conducting this experiment we ran into a few issues, but were able to successfully
use DOE on an experiment of our own design. When designing this model and procedure we
initially chose 2 hours as the time period for analysis. At first this did not seem like it would take
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a long time, but when you factor in brewing for each run then cleaning, time adds up. The
effects of this are potentially a result in the last run of the experiment were we identified an
outlier. If we were able to redesign our experiment we would likely avoid such experiment that
takes a while to obtain results. However, running an experiment of sorts showed us some of the
realities that companies face when conducting DOE. Overall, we are satisfied with the results
and implementation of DOE and we now know how to keep our coffee the hottest when
spending many hours in the library or staying up late to conduct experiments of this sort.
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Appendix
A: Initial with Outlier Value Included (16 Runs)
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B: Outlier Value Removed (15 Runs)
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C: Outlier Value Redone (16 Runs)
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D: Minitab Output Outlier Redone
Factorial Fit: Response versus Container, Brewing Type, Creamer, Sugar
Estimated Effects and Coefficients for Response (coded units)
Term
Effect Coef SE Coef
T P
Constant
128.512 0.2092 614.19 0.000
Container
-1.525 -0.762 0.2092 -3.64 0.015
Brewing Type
5.725 2.862 0.2092 13.68 0.000
Creamer
1.725 0.863 0.2092 4.12 0.009
Sugar
-0.750 -0.375 0.2092 -1.79 0.133
Container*Brewing Type 0.325 0.163 0.2092 0.78 0.473
Container*Creamer
0.825 0.412 0.2092 1.97 0.106
Container*Sugar
-0.500 -0.250 0.2092 -1.19 0.286
Brewing Type*Creamer 0.475 0.238 0.2092 1.14 0.308
Brewing Type*Sugar
1.250 0.625 0.2092 2.99 0.031
Creamer*Sugar
1.000 0.500 0.2092 2.39 0.062
S = 0.836959 PRESS = 35.8656
R-Sq = 97.98% R-Sq(pred) = 79.31% R-Sq(adj) = 93.94%
Analysis of Variance for Response (coded units)
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Source
DF Seq SS Adj SS Adj MS F P
Main Effects
4 154.557 154.557 38.6394 55.16 0.000
2-Way Interactions 6 15.297 15.297 2.5496 3.64 0.089
Residual Error
5 3.503 3.503 0.7005
Total
15 173.357
Unusual Observations for Response
Obs StdOrder Response Fit SE Fit Residual St Resid
6
15 134.600 133.663 0.694 0.937 2.00R
R denotes an observation with a large standardized residual.
Estimated Coefficients for Response using data in uncoded units
Term
Coef
Constant
128.512
Container
-0.762500
Brewing Type
2.86250
Creamer
0.862500
Sugar
-0.375000
Container*Brewing Type 0.162500
Container*Creamer
0.412500
Container*Sugar
-0.250000
Brewing Type*Creamer 0.237500
Brewing Type*Sugar
0.625000
Creamer*Sugar
0.500000
Predicted Response for New Design Points Using Model for Response
Point Fit SE Fit
95% CI
95% PI
1 121.937 0.694 (120.154, 123.721) (119.143, 124.732)
2 131.287 0.694 (129.504, 133.071) (128.493, 134.082)
3 127.612 0.694 (125.829, 129.396) (124.818, 130.407)
4 128.762 0.694 (126.979, 130.546) (125.968, 131.557)
5 125.012 0.694 (123.229, 126.796) (122.218, 127.807)
6 133.663 0.694 (131.879, 135.446) (130.868, 136.457)
7 126.512 0.694 (124.729, 128.296) (123.718, 129.307)
8 131.787 0.694 (130.004, 133.571) (128.993, 134.582)
9 127.037 0.694 (125.254, 128.821) (124.243, 129.832)
10 131.663 0.694 (129.879, 133.446) (128.868, 134.457)
11 132.787 0.694 (131.004, 134.571) (129.993, 135.582)
12 125.437 0.694 (123.654, 127.221) (122.643, 128.232)
13 131.287 0.694 (129.504, 133.071) (128.493, 134.082)
14 126.537 0.694 (124.754, 128.321) (123.743, 129.332)
15 129.762 0.694 (127.979, 131.546) (126.968, 132.557)
16 125.112 0.694 (123.329, 126.896) (122.318, 127.907)
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Effects Plot for Response
Alias Structure
I
Container
Brewing Type
Creamer
Sugar
Container*Brewing Type
Container*Creamer
Container*Sugar
Brewing Type*Creamer
Brewing Type*Sugar
Creamer*Sugar
E: Response Plots
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