Project Report
Design of Experiments – IEE 572
Experimental Design and Analysis
Exploring Efficient Heating Containers
For Use in Microwave Ovens
Instructor: Dr. Douglas Montgomery
Presented by
Can Cui
He Peng
Zohair Zaidi
(All from 4:30class)
1. Executive Summary
The objective of our experiment is to seek the combination of container factors that minimizes time consumed
to heat the substance inside to reach desired temperature.
Our choice of factors: material type, container shape, material color, and cover status, composed the treatments
investigated in our experiment. The nature of the experiment resulted in thermometer-measured observations of
temperature as response variables which are obtained by heating the substance in the container in the same time
interval.
The experimental design chosen was a factorial 24 Randomized Complete Block Design (RCBD) with one
block factor. The design matrix for the experiment was generated through a Custom Design in JMP and DesignExpert and the Fit Model analysis tool provided the output to support the documented conclusions.
2. Problem Recognition
2.1 Introduction
For many decades now since the early 1950’s, microwave ovens have been commonly used in household
kitchens to heat up and cook a variety of food and liquids. The microwave oven started off as being a giant 6 ft
750 lb machine but after many years of research and design improvements, it now finds itself being able to be
placed in almost any kitchen décor. However, despite all the research that has gone into improving the design of
the microwave oven, little thought has been given to the selection of the most efficient choice of material used
as a container for heating.
In this experiment we will be attempting to optimize the conditions for the ideal heating container that can be
used in a microwave and provide the best statistical results.
2.2 Motivation
Since currently most people do not follow any good design for heating substances in the microwave, a lot of
energy and time is wasted which has a huge negative impact on the environment. Through the implementation
of our designed experiment, we can potentially save a lot of energy and revolutionize the way people heat up
their food and drinks.
2.3 Objective
The objective of our experiment is to determine which factors significantly affect the efficiency of heating
inside a microwave. Once those factors are recognized, then we want to optimize the factors such that the
amount of time used to heat a substance is minimized and thereby the amount of energy consumed in heating is
reduced.
3. Choice of Factors
The four container factors we hypothesize are most important with respect to overall optimization include:
material type, container shape, material color, and cover status. These four factors compose the experimental
factors we wish to study in our experiment. Table 1 list these factors along with the chosen levels for each.
The potential factors that we are considering for our design are as follows:
Factor
Type of Material
Shape
Color
Cover
Table 1: Experimental factors and levels
Level 1
Plastic
Cylinder
Clear
Open
Level 2
Glass
Rectangle
Opaque
Closed
4. Description of Factors
4.1 Type of Material
The two types of materials we chose to test in this experiment are plastic and glass. These materials were
chosen because they are most commonly used as containers among housewives. We think the type of material
makes a significant difference in the efficiency of heating because of the difference in material absorption of
microwaves.
4.2 Shape
The shapes of container we chose to test are cylinder and rectangle. These shapes were chosen due to them
being used in drinking containers and in sandwich boxes. We believe the shape will have a significant
difference in heating efficiency because since they are very distinct in form and open area, the directions by
which the microwaves will reach the substance will differ significantly, potentially affecting the rate of heating.
4.3 Color
We will be using two types of colored containers – clear and opaque. The color of the container should make a
significant difference in heating efficiency because of the relationship between the color of a material and the
wavelengths it absorbs or transmits. Therefore it is possible that a certain type of color tends to absorb
microwaves better than others.
4.4 Cover
The last factor chosen was whether or not the container will be covered. It is known that when a container is
covered, it will keep heat from escaping from the container. But at the same time, it may also impede the flow
of additional microwaves into the container. Since the relative rates of both are not known, it is imperative to
test this factor and determine which one plays a more important role in heating efficiency.
5. Selection of Response Variable
Temperature is the response variable selected that will be used to determine which combination of factors allow
for most efficient heating inside of a microwave. The initial temperature will be held constant for all runs and
then immediately after the samples are processed in the microwave, the final temperature will be measured for
all samples using a digital thermometer to ensure accuracy of the measurements.
The experimental design chosen was a factorial 24 Randomized Complete Block Design (RCBD) with one
block factor, the type of substance being heated. The substances chosen in the block were water and milk to
ensure that the type of substance does not interact with the container and the change in temperature are truly due
to the effect of the factors relating to the container. The design matrix for the experiment was generated through
a Custom Design in JMP. The experimental worksheet is provided below:
Table 2: JMP Experimental Design Worksheet
Run
1
2
3
4
5
6
7
8
Block
Water
Water
Water
Water
Water
Water
Water
Water
Material
Glass
Glass
Plastic
Plastic
Plastic
Plastic
Plastic
Plastic
Shape
Cylinder
Rectangle
Rectangle
Cylinder
Rectangle
Cylinder
Rectangle
Cylinder
Color
Opaque
Clear
Clear
Opaque
Opaque
Opaque
Clear
Clear
Cover
Closed
Closed
Open
Open
Closed
Closed
Closed
Closed
Temperature
.
.
.
.
.
.
.
.
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Water
Water
Water
Water
Water
Water
Water
Water
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Glass
Glass
Plastic
Plastic
Glass
Glass
Glass
Glass
Glass
Glass
Plastic
Glass
Glass
Plastic
Plastic
Glass
Plastic
Glass
Glass
Plastic
Plastic
Glass
Plastic
Plastic
Cylinder
Cylinder
Rectangle
Cylinder
Rectangle
Cylinder
Rectangle
Rectangle
Cylinder
Rectangle
Cylinder
Rectangle
Rectangle
Cylinder
Cylinder
Cylinder
Rectangle
Rectangle
Cylinder
Cylinder
Rectangle
Cylinder
Rectangle
Rectangle
Clear
Clear
Opaque
Clear
Opaque
Opaque
Clear
Opaque
Clear
Opaque
Opaque
Clear
Clear
Clear
Opaque
Opaque
Clear
Opaque
Opaque
Clear
Opaque
Clear
Opaque
Clear
Closed
Open
Open
Open
Open
Open
Open
Closed
Open
Open
Closed
Closed
Open
Open
Open
Open
Open
Closed
Closed
Closed
Open
Closed
Closed
Closed
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
6. Performing the experiment
We prepared eight categories of containers which are listed in Table 2. The measuring tool we used is an
electronic infrared thermometer which has a decimal accuracy. Please see the Appendix for the pictures of
containers and microwave oven and electronic infrared thermometer. There are two blocks, one is water, and
the other is milk. We performed the experiment in the same day. First, we did experiment with water which is
contained in a big plastic container to ensure unique water resource and to minimize the variation of the water
temperature. Moreover, we measured the temperature of water before each run so we can keep records of how
much the temperature differs after being heated instead of a single temperature value after heating which makes
the experiment more precise. Therefore, response in this experiment is the temperature difference instead of the
temperature after heating. To minimize the variation of microwave oven temperature between each run, we
cooled down the environment inside the oven by fanning after heating, and started next run until the
temperature dropped to normal value. For the experiment with milk, we did exactly the same routine as with
water.
The result of experiment is shown in table 3.
Table 3: Measured Data Result
Befor Afte
Run
Block
Material
Shape
Color
Cover
e
r
Difference
85.2
58.8
1
Water
Glass
Cylinder
Opaque
Closed
26.4
75.7
51.3
2
Water
Glass
Rectangle
Clear
Closed
24.4
83
58.9
3
Water
Plastic
Rectangle
Clear
Open
24.1
85.2
61.6
4
Water
Plastic
Cylinder
Opaque
Open
23.6
81
54.3
5
Water
Plastic
Rectangle
Opaque
Closed
26.7
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Milk
Plastic
Plastic
Plastic
Glass
Glass
Plastic
Plastic
Glass
Glass
Glass
Glass
Glass
Glass
Plastic
Glass
Glass
Plastic
Plastic
Glass
Plastic
Glass
Glass
Plastic
Plastic
Glass
Plastic
Plastic
Cylinder
Rectangle
Cylinder
Cylinder
Cylinder
Rectangle
Cylinder
Rectangle
Cylinder
Rectangle
Rectangle
Cylinder
Rectangle
Cylinder
Rectangle
Rectangle
Cylinder
Cylinder
Cylinder
Rectangle
Rectangle
Cylinder
Cylinder
Rectangle
Cylinder
Rectangle
Rectangle
Opaque
Clear
Clear
Clear
Clear
Opaque
Clear
Opaque
Opaque
Clear
Opaque
Clear
Opaque
Opaque
Clear
Clear
Clear
Opaque
Opaque
Clear
Opaque
Opaque
Clear
Opaque
Clear
Opaque
Clear
Closed
Closed
Closed
Closed
Open
Open
Open
Open
Open
Open
Closed
Open
Open
Closed
Closed
Open
Open
Open
Open
Open
Closed
Closed
Closed
Open
Closed
Closed
Closed
23.5
22.4
23.0
23.8
23.6
26.7
23.5
23.3
26.5
25.0
23.9
24.0
21.0
13.4
14.9
16.6
16.6
16.2
19.1
19.2
18.7
19.3
19.5
15.2
19.9
17.2
18.5
85.5
83.6
82.9
80.1
83.3
76
84.9
81.9
85.9
77.5
78.1
86.6
87.5
82.3
74
79
98.4
85.4
81.4
86.2
84.3
83.3
95.5
76.9
80.5
80.1
82.7
62.0
61.2
59.9
56.3
59.7
49.3
61.4
58.6
59.4
52.5
54.2
62.6
66.5
68.9
59.1
62.4
81.8
69.2
62.3
67.0
65.6
64.0
76.0
61.7
60.6
62.9
64.2
7. Statistical analysis of the data (Using both JMP and Design-Expert)
7.1 Temperature Response
Table 4: Summary of Fit
RSquare
0.846565
RSquare Adj
0.773501
Root Mean Square Error
3.194174
Mean of Response
61.69375
Observations (or Sum Wgts)
32
The R-squared value indicates how much of the total variation is explained by the regression model. It is
possible sometimes this value to be inflated due to large number of factors included in the model, therefore a Rsquared adjusted value is also calculated which takes into consideration the number of factors included in the
model. In this case, 77.3% of the variation can be explained by the constructed model of the chosen factors,
which is relatively good and gives confidence to the models ability in capturing the source of variation in the
factors that we have chosen.
7.2 Factor Evaluation
Term
Intercept
Materials[Plastic]
Shape[Cylinder]
Colors[Clear]
Cover[Open]
Materials[Plastic]*Shape[Cylinder]
Materials[Plastic]*Colors[Clear]
Materials[Plastic]*Cover[Open]
Shape[Cylinder]*Colors[Clear]
Shape[Cylinder]*Cover[Open]
Colors[Clear]*Cover[Open]
Table 5: Parameter Estimates
Estimate
Std Error
61.69375
4.23125
2.075
0.564656
2.3375
0.564656
0.4875
0.564656
0.4875
0.564656
1.49375
0.564656
2.04375
0.564656
-0.39375
0.564656
0.26875
0.564656
0.23125
0.564656
0.61875
0.564656
DFDen
1
20
20
20
20
20
20
20
20
20
20
t Ratio
14.58
3.67
4.14
0.86
0.86
2.65
3.62
-0.70
0.48
0.41
1.10
Prob>|t|
0.0436*
0.0015*
0.0005*
0.3982
0.3982
0.0155*
0.0017*
0.4936
0.6393
0.6865
0.2862
From the p-values generated by JMP using the custom factorial model, it is evident that the significant factors in
this experiment are Materials, Shape, Materials & Shape interaction, and Materials & Color interaction. Once
the p-value goes below a certain value determined from the t-table and degrees of freedom, the factors can be
declared as being significant.
ANOVA for selected factorial model
Table 6: Analysis of variance table [Partial sum of squares - Type III]
Source
Sum of
Mean
F
p-value
Squares
df
Square
Value
Prob > F
Block
575.17
1
575.17
Model
527.03
5
105.41
11.36
< 0.0001
significant
A-Materials
138.33
1
138.33
14.91
0.0007
B-Shape
174.53
1
174.53
18.82
0.0002
C-Colors
7.74
1
7.74
0.83
0.3698
AB
71.40
1
71.40
7.70
0.0103
AC
135.03
1
135.03
14.56
0.00 08
Residual
231.87
25
9.27
Cor Total
1334.07
31
The results are further corrobarated by running the analysis in Design Expert and from the F-values, the same
factors can be seen as significant. The F-statistic is calculated by taking the proportion of the mean square of the
factor by the mean square of the residual. Thus, the higher the value of mean square, the more significant the
factor can be seen to be. In this case, it appears that the main effect Shape has the highest mean square and
perhaps is the most significant factor.
Design-Expert?Software
Temperature
Shapiro-Wilk test
W-value = 0.911
p-value = 0.286
A: Materials
B: Shape
C: Colors
D: Cover
Positive Effects
Negative Effects
Half-Normal Plot
H a lf- N o r m a l % P r o b a b ility
Error estimates
99
B
95
A
AC
90
AB
80
70
C
50
30
20
10
0
0.00
1.17
2.34
3.50
4.67
|Standardized Effect|

Figure 1 Half-Normal Plot
The half-normal probability plot is a visual way of identifying which factors are singificant in an experiment.
The plot takes the absolute value of effect estimates and plots it against their normal probabilites in a
cumulative manner. Those effects which are significant will be plotted far away from the straight line that
crosses the origin. Thus the same factors which were identified through the p-values and F-statistic are found to
be significant here, A (Materials), B(Shape), AB(Material/Shape Interaction), and AC(Materials/Colors
interaction.
Final Equation in Terms of Coded Factors:
Temperature
=
+61.69
+2.08
+2.34
-0.49
+1.49
-2.05
*A
*B
*C
*A*B
*A*C
Once the significant factors are identified, an equation can be constructed for the model using the effect
coefficients calculated in the table above. This equation can then be used to predict values according to generate
prediction values that will later be used in residual analysis to test the validity of the assumptions made about
this experiment.
7.3 Effect of blocking
Table 7: REML Variance Component Estimates
Random Effect Var Ratio
Var Component
Random Block 3.4470394 35.169281
Residual
10.20275
Total
45.372031
-2 LogLikelihood = 150.52238998
Std Error
50.63908
3.2263928
95% Lower
-64.08149
5.9718276
95% Upper
134.42005
21.276169
Pct of Total
77.513
22.487
100.000
According to the whole effect of the system, the block plays a really important role during the experiment.If let
the system ignore the block affect and just put 4 factors in the system, the R-squared adjusted value is lower
than 30% which reduce the confidence of this model a lot and the majority of variance would not be explained.
So setting up this block is a right choice.
Effect Details Random Block
Table 8: Least Squares Means Table
Level
Milk
Water

Least Sq Mean
65.849647
57.537853
Std Error
0.79498041
0.79498041
Figure 2 LS Means and Block Plot
This figure indicates that the material of liquids makes a lot of difference in the change of temperature. This is
reasonable in physics. The heat capacities of milk and water are 0.94 vs 1.0. According to the equation of heat
capacity,
which shows the linear relative between capacity and temperture. Since milk have lower heat
capacity, and assume they get same quantity of heat, milk should have higher change of temperature than water
should have. The result of experiment is fit for the theory.
7.4 Residual Analysis
Design-Expert?Software
Temperature
49.3
Normal Plot of Residuals
N o r m a l % P r o b a b ilit y
Color points by value of
Temperature:
81.8
99
95
90
80
70
50
30
20
10
5
1
-3.00
-2.00
-1.00
0.00
1.00
Internally Studentized Residuals

Figure 3 Normal Plot of Residuals
2.00
3.00
Design-Expert?Software
Temperature
Color points by value of
Temperature:
81.8
49.3
In te r n a lly S tu d e n tiz e d R e s id u a ls
Analyzing the residuals is an important way to verify the assumptions to determine whether the results from the
factorial analysis can be depended upon. The first assumption that is made is that the data comes from a
population of normal distribution. To check this assumption, a normal probability plot is constructed from the
residuals. If the assumption is met, then the residuals should all fall on a straight line with little deviation. In this
case, the majority of the residuals seems to fall in line with only few points which seem to be outliers and
should not significantly affect our data, therefore we can conclude there are no alarming problems with
normality.
Residuals vs. Predicted
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
50.00
55.00
60.00
65.00
70.00
75.00
Predicted
Design-Expert?Software
Temperature
Color points by value of
Temperature:
81.8
49.3
In te r n a lly S tu d e n tiz e d R e s id u a ls

Figure 4 Residuals vs. Predicted Plot
Residuals vs. Run
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
1
6
11
16
21
26
31
Run Number

Figure 5 Residuals vs. Run Plot
A second way to confirm that the model chosen is correct and that the assumptions is met is to plot the residuals
by the predicted values and by the run. The predicted values are generated from the equation that is created
from the effect coefficients of the significant factors as was shown previously. If the assumptions are met, then
both plots should be structureless and show no apparent pattern or correlation between the points. Indeed such is
the case for both plots, with only slight deviation in the first plot, further confirming that our model is correct
and that there is nothing major to worry about in terms of reliability of our analysis.
Design-Expert?Software
Temperature
Predicted vs. Actual
Color points by value of
Temperature:
81.8
90.00
49.3
P r e d ic te d
80.00
70.00
60.00
50.00
40.00
40.00
50.00
60.00
70.00
80.00
90.00
Actual

Figure 6 Predicted vs. Actual Plot
Another way to see how well the model fits the data is to directly compared the predicted values versus the
actual values that were obtained by the experiment. If the model is a first-order model and there is a complete
fit, then the points should all fall along the straight line. In this case, there is some variance between the
predicted and actual values, but relatively speaking there is a good fit. Usually there is always some skewing
that occurs at the extreme ends, in this case at the extremely low and high temperatures, hence the appearance
of an s-shaped curve.
7.5 Variance Analysis
Color points by
Standard Order
32
1
In te r n a lly S tu d e n tiz e d R e s id u a ls
Design-Expert?Software
Temperature
Residuals vs. Block
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
1.00
1.20
1.40
1.60
1.80
2.00
1.80
2.00
Block
Design-Expert?Software
Temperature
Color points by
Standard Order
32
1
In te r n a lly S tu d e n tiz e d R e s id u a ls

Figure 7 Residuals vs. Block Plot
Residuals vs. Materials
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
1.00
1.20
1.40
A:Materials

Figure 8 Residual vs. Materials Plot
1.60
Color points by
Standard Order
32
1
In te r n a lly S tu d e n tiz e d R e s id u a ls
Design-Expert?Software
Temperature
Residuals vs. Shape
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
1.00
1.20
1.40
1.60
1.80
2.00
1.80
2.00
B:Shape
Design-Expert?Software
Temperature
Color points by
Standard Order
32
1
In te r n a lly S tu d e n tiz e d R e s id u a ls

Figure 9 Residual vs. Shape Plot
Residuals vs. Colors
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
1.00
1.20
1.40
1.60
C:Colors

Figure 10 Residual vs. Colors Plot
Color points by
Standard Order
32
1
In te r n a lly S tu d e n tiz e d R e s id u a ls
Design-Expert?Software
Temperature
Residuals vs. Cover
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
1.00
1.20
1.40
1.60
1.80
2.00
D:Cover

Figure 11 Residual vs. Cover Plot
The Figure above shows nothing very unusual in the experiment. All the residual in absolute value is lower than
the standardized value 3.00. And the distribution between positive value and negative value is random and has
no tendency to be one side.
Have to mention that there is a mild tendency to increase or decrease from left side to right side, however, the
problem is not severe enough to have a dramatic impact on the analysis and conclusions.
7.6 Factors Interaction
Design-Expert?Software
Factor Coding: Actual
Temperature
Interaction
Design Points
X1 = A: Materials
X2 = B: Shape
B1 Rectangle
B2 Cylinder
75
T e m p e ra tu re
Actual Factors
C: Colors = Opaque
D: Cover = Closed
B: Shape
80
70
65
60
55
50
Glass
Plastic
A: Materials

Figure 12 Material-Shape Interaction Plot
Interaction plots generated by JMP are a good way to see the effect of each factor relative to another factor.
Since the Material and Shape factors were significant they are varied and the other two factors that are not
significant are held constant. It can be seen that in the case of cylinder made of plastic, there is an increase in
temperature whereas in the case of glass, it decreases for plastic.
Design-Expert?Software
Factor Coding: Actual
Temperature
Interaction
Design Points
X1 = A: Materials
X2 = B: Shape
B1 Rectangle
B2 Cylinder
75
T e m p e ra tu re
Actual Factors
C: Colors = Clear
D: Cover = Closed
B: Shape
80
70
65
60
55
50
Glass
Plastic
A: Materials

Figure 13 Material-Shape Interaction Plot
If the color is then changed from opaque to clear, we see further improvements in the slope between the glass
and plastic, indicating that results are better when using a container that is both plastic and clear in color. It’s
also interesting to note that the slope changes to positive in the case of the rectangle, though it is still quite
below the results obtained using a cylinder.
Design-Expert?Software
Factor Coding: Actual
Temperature
Interaction
B: Shape
90
Design Points
X1 = A: Materials
X2 = B: Shape
B1 Rectangle
B2 Cylinder
80
T e m p e ra tu re
Actual Factors
C: Colors = Opaque
D: Cover = Open
70
2
60
50
40
Glass
Plastic
A: Materials

Figure 14 Material-Shape Interaction Plot
When the container is then open and opaque, there seems little difference between the glass and plastic cases,
indicating this combination is not effective in improving temperature results.
Design-Expert?Software
Factor Coding: Actual
Temperature
Interaction
B: Shape
90
Design Points
X1 = A: Materials
X2 = B: Shape
80
T e m p e ra tu re
Actual Factors
C: Colors = Clear
D: Cover = Open
B1 Rectangle
B2 Cylinder
70
2
60
50
40
Glass
Plastic
A: Materials

Figure 15 Material-Shape Interaction Plot
In the case of clear and open, we see that in the glass case there is possible interaction that may occur, but it is
not close enough to be declared an interaction.
Design-Expert?Software
Factor Coding: Actual
Temperature
Interaction
C: Colors
90
Design Points
X1 = A: Materials
X2 = C: Colors
C1 Clear
C2 Opaque
80
T e m p e ra tu re
Actual Factors
B: Shape = Rectangle
D: Cover = Open
70
60
50
40
Glass
Plastic
A: Materials

Figure 16 Material-Colors Interaction Plot
When we then switch the constant variable to become the shape and vary the material and color, we can see that
there is a clear interaction that is occurring between the material and color. This is a clear example of why it’s
important to look at interaction plots to see which factors are affected by other factors.
7.7 The Best Combination of Our Experiment
As Figure shown below, the highest difference of temperature 70.1458 is obtained by the combination of plastic
as material, clear as color and cylinder as shape and open as cover. As we have concluded, among all four
factors, only material, shape, interaction of material and shape and interaction of material and color are
significant. Therefore, whether the cover is open or closed does not make a lot of influence to the temperature
increasing. This can also be noticed by directly observing the experimental result:
Table 8: Partial Measured Data Result
Befor Afte
Run
Block
Material
Shape
Color
Cover
e
r
Difference
82.9
59.9
7
Water
Plastic
Cylinder
Clear
Closed
23.0
84.9
61.4
12
Water
Plastic
Cylinder
Clear
Open
23.5
98.4
81.8
22
Milk
Plastic
Cylinder
Clear
Open
16.6
95.5
76.0
28
Milk
Plastic
Cylinder
Clear
Closed
19.5
There is only 1.5°F and 5.8°F difference respectively in experiments with water and milk and as the number of
replicates increases, the difference is supposed to decrease. In conclusion, the best combination of factor levels
is “plastic, cylinder, clear and open”.
Design-Expert?Software
Factor Coding: Actual
Temperature
X1 = A: Materials
X2 = B: Shape
X3 = C: Colors
Cube
Temperature
2
62.0167
65.0542
2
Actual Factor
D: Cover = Open
2
58.8917
B: Shape
B+: Cylinder
70.1458
2
2
60.3333
57.3958
2
C+: Opaque
C: Colors
2
B-: Rectangle
57.2083
A-: Glass

2
A: Materials
C-: Clear
62.4875
A+: Plastic
Figure 17 Cube
8. Conclusion
In this experiment we attempted to optimize the conditions for the ideal heating container that can be used in a
microwave oven and provide the best statistical results. The experimental design chosen was a factorial 24
Randomized Complete Block Design (RCBD) with the type of substance being heated as a block factor. We
analyzed the outputs in JMP and Design Expert which provided us several comprehensive analyses such as,
ANOVA table, half-normal probability plot, normal plot of residuals, residuals vs predicted and residuals vs
runs…
Finally, we concluded that the best combination of factor levels is “plastic, cylinder, clear and open”.
This experiment is very meaningful because through the implementation of our designed experiment, we find
the most efficient way that can potentially save a lot of energy and revolutionize the way people heat up their
food and drinks. Due to the limitation of our time and energy, we did only one replicate. In the future, we could
do more replicates and also add more factors thus make our experimental results more reliable.
9. Appendix:
Microwave oven
Thermometer
Some of Containers