report doe2
TRANSCRIPT
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CHAPTER 1 : INTRODUCTION
1.0 PROJECT BACKGROUND
Nowadays, pop corn can be made even without the popcorn maker. There
are other ways like using microwave and saucepan1. In this research, we are
focusing on making popcorn by using microwave. Microwave is used instead of
saucepan is due to the result of our brainstorming session which is guided by the
SMART analysis. Figure 1.1 show the result of SMART analysis between
saucepan and microwave. The end result while making popcorn is to have high
number of popped corn compare to the un-popped corn. A study2 in 1993 was
conducted to find out the factors that influence the number of popped corn.
However, the finding is concluded as a failure as there is no significance factors
are found. This study will benchmark the factors used by the previous study and
brainstorm among the members to identify the variables that might influence the
result of popped-corn.
S M A R TMicrowave / / / / /
Saucepan x / x x x
Figure 1.1: SMART analysis on Popcorn making
1.1 PROBLEM STATEMENT
There are lots of kernels in the market that come out with different packaging and
instruction on the packaging on how making the popcorn (Appendix1). The
problem is does the instruction given will produce the high number of popped
1Kookies, How to make popcorn without a popcorn maker, 2009,
(answers.yahoo.com/quation/index?qid=20090227105628AA0wdpW)2
Applying DOE to microwave popcorn, Mark. J. Anderson and Hank P. Anderson (1993)
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corn as wanted by the maker?. What is the right combination that can boost up the
number of popped-corn.
1.2 OBJECTIVE
1.2.1 Identify factors that affect the end result of the pop-corn making.
1.2.2 Recommending the best combination of factor in pop-corn making.
1.2.3 Develop the regression equation to predict the CTQ (Response variable)
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CHAPTER 2 PARAMETER SELECTION
2.0 FACTOR, LEVEL AND RESPONSE SELECTION
2.1 As mention in chapter 1, we benchmark the factors used in the previous study2
and brainstorm on the factors that might influence the yield of the popcorn. Figure 1.2
shows the Fishbone Diagram that sum up the output of the brainstorming session. After
that, we come out with Cause and Effect matrix (Figure 1.3) to identify and select the
factors.
Figure 1.2: The Fishbone Diagram
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Key
Process
Output
Variables
Business
Importance10
Rank 1
1
Process Step KPIVPoppe
d-Corn
R
ank
Process
Ste
ps
&
Key
Process
Input
Variables
1 Put Kernels on the Paper Bag Brand/Price 9 1
2Use of
Margarines9 1
3 Preheat 1 2
4 Tray Elevate 9 1
5 Setting on the microwave Temperature 9 1
6Time
Cooking9 1
7Surrounding
Temperature9 1
Reverse
Score10
Reverse
Rank1
Figure 1.3 : Cause and Effect Matrix
2.2 Two level will be used which are low (-) and high (+). The low level is believed
to give low impact while the high level is believed to give high impact. The level is set
based on information on given on the packaging (Appendix 1) and also the level stated by
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the previous study. The additional factor which is margarine is derived from the
information on simple.recipe (appendix 2) which required the used of oil to enhance the
yield of the corn. Figure 1.4 shows the parameters which include the factors and level
that will be used in this experiment.
FACTOR LEVEL (-) LEVEL (+)
TEMPERATURE
Medium High
TRAY
ELEVATE
MARGARINE
COOKING
TIME
2 Minute 3 Minute
PRICE/BRAND
Figure 1.4 Level set up
2.3 As a popcorn maker, the number of less un-popped is wanted by the maker. In
this study, the response or the CTQ will be the weight (g) of un-popped corn left after theprocess of popcorn making take place. In this experiment, the flour weight scale with the
resolution 0.01 is used. The small resolution is used in order to avoid human error while
reading the weight of the kernels. See Figure 1.5
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Figure 1.5 Weight Scale
Figure 1.6 The factors and response of Pop Corn Making
POP CORN MAKING
100gram corn bullets
Power supply
Weight of un-popped
corn (g)
Temperature
CookingTime
TrayElevate
Margarine
Brand/Price
Surrounding
heat
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CHAPTER 3 EXPERIMENTAL DESIGN
3.0 EXPERIMENTAL DESIGN
As mention in previous chapter, there are 6 factors chosen. Five (5) factors
that can be controlled while one (1) factor cannot be control which is surrounding
heat. Hence, to see is there any significant different on surrounding heat, we
decide to block the experiment by using day and night with the justification that
the heat on day is higher than night heat. In order to avoid the existing heat of
microwave affecting the reading of the next experiment, after every experiment,
the microwave is left to be cooled for 10 minutes.
The full experiment need to be conducted in this project is 25
= 32 which
derived from the formula of full factorial nk. To avoid any error on measuring and
experiment we decide to run the experiment with 3 replication and 3 repetitions.
However, the total experiment need to be run is 3(25) = 96 times which too many.
Hence, we decide to use fractional factorial with quarter experiment with 3
repeated measure and 3 replication which give 3(25-2) = 24 times of experiment.
The quarter is chose instead of half is due to below justification:
3.0.1 Limited resources
Conducting 96 experiments required lots of kernels, margarine,
paper bag and other resources which are a waste for the
experimenter. Beside, long time consuming will be required and
experimenter cannot fulfill it due to other commitment.
3.0.2 Capabilities/Durability of Machine (Microwave)
The capabilities of the microwave are limited to little extent.
Excess usage of the microwave might blow up the microwave.
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The fractional factorial is used to screen out important factors. Full factorial will
be conducted after unimportant factors is screened out so that the factors can be analyzed
without any confounded or aliased. Figure 1.7 shows the process flow of this experiment.
Figure 1.7 Flow Chart of Experiment
START
Fractional
Factorial (25-2)
Identify
Significance
Factors
Screen out
important factors
Conduct Full
Factorial (2k)
ANALYZE
Y
Re-level
N
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CHAPTER 4 CONDUCT THE EXPERIMENT
4.0 CONDUCTING THE EXPERIMENT
4.1 Fractional Factorial
4.1.1 The Table 4.1 below show the matrix diagram for fractional factorial, 25-2
been conducted. The experiment below is blocked with Day and Night.
It randomizely done. The result below represent the average from 3
repeated measure and 3 replications.
4.1.2 This 25-2 experiment is having Resolution III confounding which means
that:
4.1.2.1There is no main effect is confounded with another main effect
4.1.2.2Main effect are confounded with two-factors interaction
4.1.3 The confounding for this 25-2 popcorn experiment are as below:
4.1.3.1 I + ABD + ACE + BCDE
4.1.3.2 A + BD + CE + ABCDE
4.1.3.3 B + AD + CDE + ABCE
4.1.3.4 C + AE + BDE + ABCD
4.1.3.5 D + AB + BCE + ACDE
4.1.3.6 E + AC + BCD + ABDE
4.1.3.7 BE + CD + ABC + ADE
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CHAPTER 5 ANALYSIS
5.0 ANALYZING THE FRACTIONAL FACTORIAL EXPERIMENT
All the analyzing that is proven by Minitab is attached to this report as an appendix.
5.1 Normality Test
Normality test is used to make sure the distribution of the data gain from the
experiment by using Minitab 1.5.
Ho : The data is normally distributed
HA : The data is not normally distributed
Based on the result of the normality test, p-value is equal to 0.0850 which is
greater than 0.05, so the null hypothesis is fail to reject. Thus, the data is normally
distributed.
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78)/4
= 62.23
Table 4.2 : Main Effect of the Factors
Figure 1.8 Main Effect Plot
Based on the main effect plot, we identify three important factor which is the
Brand/Price, Cooking Time and Temperature. Full factorial experiment is
conducted through the use of these 3 factors. Before conducting the full factorial,
we test the significant of these three factors to ensure that the level is used
correctly. Table 4.3 shows the result of the significance test.
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Factors Hypothesis Result (paired t-test)
T =
; p < 0.05
reject the null
hypothesis
Brand/Price Ho : There is no significance
different between branded and low
brand of kernels towards the output
HA : There is significance
different between branded and low
brand of kernels towards the output
P = 0.221
Null hypothesis is failed
to reject as p is greater
than 0.05.
There is no significance
different on branded low
brand kernels
Temperature Ho : There is no significance
different between medium and high
temperature towards the output of
kernels
HA : There is significance
different medium and high
temperature towards the output of
kernels
P = 0.019
Null hypothesis is
rejected as p is less than
0.05.
There is significance
different on high and
medium temperature
Time Ho : There is no significance
different between 2 minutes and 3
minutes towards the output of
kernels
HA : There is significance
different between 2 minutes and 3minutes towards the output of
kernels
P = 0.338
Null hypothesis is fail to
reject as the p value is
greater than 0.05 .
There is no significance
different on 2 minutesand 3 minutes
Figure 4.3 Result of paired t-test on selected factors
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As the cooking time is not significant, we decide to increase the level for full
factorial experiment.
The significance of Day and Night also been measured to identify whether the
surrounding heat gives impact towards the yield of the corn by using two t-test.
The result of the two t-test is shown in the Table 4.4
Hypothesis Result two t-test
T =
; p
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Temperature
Cooking
Time3 minutes 1.5 minutes
Figure 4.5 Factors and Level of full factorial experiment.
5.3.1 The Cooking Time is once again taken as factors even the result in the
fractional factorial shows it is significance due to the reason on finding if
the popcorn can be make faster (low cooking time) with good amount of
unpopped corn. Hence, in this full factorial, we adjusted the level of Time
from 2 minutes and 3 minutes into 1.5 minutes to 3 minutes.
5.3.2 The same step is repeated. Figure 1.9 shows the matrix diagram for full
factorial experiment and its result (gram). 23
= 8 experiment is runs with
three (3) repeated measures and 3 replications. The figure 1.9 shows the
average of the results.
Exp
No
Run
Order
Brand/Price Cooking
Time
Temperature CTQ (g)
1 4 ACI II 3 min High 18.0
2 6 ACI II 3 min Medium 62.5
3 2 ACI II 1.5 min High 99.0
4 8 ACI II 1.5 min Medium 100.0
5 1 TESCO 3 min High 58.5
6 7 TESCO 3 min Medium 71.5
7 3 TESCO 1.5 min High 90.0
8 5 TESCO 1.5 min Medium 100.0
Figure 1.9 Matrix Diagram of Full Factorial
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5.3.3 Normality Test
Normality test is used to ensure that the result is normally distributed.
Ho : The data is normally is distributed.
HA : The data is not normally distributed.
The p-value is equal to 0.164 which is greater than 0.05. Thus, null hypothesis is fail to
reject which means that the data is normally distributed.
5.3.4 Main Effect of Full Factorial
Main effect plot for full factorial is develop to identify the effect of each
factor towards the yield of the kernels. Figure 1.10 shows the main effect
of full factorial.
FACTORS MAIN EFFECT
Price/Brand (+) = (18 + 62.5 + 99.0 +
100) / 4
= 69.88
(-) = (58.5 + 71.5 + 90.0
+ 100)/4
(+)(-)
= 69.8880
= -10.12
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= 80
Temperature (+) = ( 18 + 99.0 + 58.5
+ 90.0)/4
= 66.37
(-) = (62.5 + 100 + 71.5
+ 100) / 4
= 83.5
(+)(-)
= 66.37-83.5
= -17.13
Cooking Time (+) = (18 + 62.5 + 58.5 +
71.5)/4
= 52.63
(-) = (99.0 + 100 + 100 +
90)/4
= 97.25
(+)(-)
= 52.63- 97.25
= - 44.63
Figure 1.10 Main Effect Plot of full factorial
5.3.5 Significance Testing of Main Effect
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Factors Hypothesis Result (paired t-test)
T =
; p < 0.05
reject the null
hypothesis
Brand/Price Ho : The branded kernels gives no
influenced to the numbers of un-
popped corn
HA : The branded kernels is
influencing the result of un-popped
corn.
P = 0.731
The p value is greater
than 0.05 so the null
hypothesis is fail to
reject.
The branded kernels
give no influence to the
yield of popped corn.
Temperature Ho : The high or low temperature
producing the equal number of
unpopped corn
HA : The high temperature give high
number of popped-corn compare to
the medium
P = 0.572
Null hypothesis is fail to
reject as the p value is
greater than 0.05.
Thus, there is no
difference in the number
of un-popped corn with
the use of high or
medium temperature.
Cooking
Time
Ho : The 3 minutes cooking time gives
same amount of 1.5 minutes un-
popped corn
HA : The 3 minutes cooking time
popped different from 1.5 minutes.
P = 0.038
Null hypothesis is
rejected as the p value is
less than 0.05.
Thus, the 3 minutes and1.5 minutes cooking
time produced different
unpopped corn amount
Table 4.6 The significance test for full factorial experiment.
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Based on the significance test conducted on the main effect plot, Time factor is
the only factor that gives significant value in this experiment. To be compare with
the fractional factorial, temperature is the significant one, however due to any
confounding; it turns to be not significant in the full factorial.
5.3.6 Interaction Plot of Full factorial
5.3.6.1Interaction plot is develop to measure or identify the interaction
between the factors. Figure 1.11 shows the interaction plot of full
factorial experiment between the three factors.
Brand
(A)
Cooking
Time (B)
Temperature
(C) CTQ (Y) AB*Y AC*Y BC*Y
ACI II
(+)
3 min
(+)
High
(+)
18 18 18 18
ACI II
(+)
3 min
(+)
Medium
(-)
62.5 62.5 - 62.5 -62.5
ACI II
(+)
1.5 min
(-)
High
(+)
99.0 - 99.0 99.0 - 99.0
ACI II
(+)
1.5 min
(-)
Medium
(-)
100 -100 -100 100
TESCO
(-)
3 min
(+)
High
(+)
58.5 -58.5 -58.5 58.5
TESCO
(-)
3 min
(+)
Medium
(-)
71.5 - 71.5 71.5 -71.5
TESCO
(-)
1.5 min
(-)
High
(+)
90.0 90.0 -90.0 -90.0
TESCO
(-)
1.5 min
(-)
Medium
(-)
100.0 100 100 100
Interaction Effect
= -
58.5/4
= -14.63
= -22.5 / 4
= - 5.63
= -46.5/4
= -11.63
igure 1.11 Interaction Effect
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Interaction Factors
BrandTime (AB) (+) (+) (18 + 62.5)/2 = 40.25
(-) ( 99 + 100) / 2 = 99.5
(-) (+) (58.5 + 71.5) / 2 = 65
(-) ( 90 + 100 ) / 2 = 95
BrandTemperature (AC) (+) (+) (18 + 99)/2 = 58.5
(-) ( 62.5 + 100) / 2 = 81.25
(-) (+) (58.5 + 90) / 2 = 74.25
(-) ( 71.5 + 100 ) / 2 = 85.75
TimeTemperature (BC) (+) (+) (18 + 58.5)/2 = 38.25
(-) ( 62.5 + 71.5) / 2 = 67
(-) (+) (99 + 90) / 2 = 94.5
(-) ( 100 + 100 ) / 2 = 100
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Figure 1.12 Interaction Plot Effect
5.3.7 Figure 1.12 shows the interaction of the factors with each other. Based on
the graph, the interaction of Brand and Cooking Time give strong
interaction effect. ANOVA will be conducted to identify the significanceof the factors interaction.
5.3.8 ANOVA
5.3.8.1Two Way ANOVA is used to identify the significance of every
interaction. Table 4.7 shows the result of the significance test.
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Factors Hypothesis Result (Two Way ANOVA), Minitab 1.5
BrandTime Ho : The interaction
between brand and time
give no significance
different to yield of
popped-corn
HA : The interaction
between brand and time
give significance different
towards the yield of
popped corn
P = 0.285
Null Hypothesis is fail to reject as the p
value is greater than 0.05.
Thus, the interaction between brand and
time is having no significance different
towards the CTQ.
BrandTemperature Ho : The interaction
between brand and
temperature give no
significance different to
yield of popped-corn
HA : The interaction
between brand and
temperature give
significance different
towards the yield of
popped corn
P = 0.831
Null hypothesis is fail to reject as the p
value is greater than 0.05.
Thus, the interaction between brand and
temperature is having no significance
different towards the CTQ
TimeTemperature Ho : The interaction
between temperature and
time give no significance
different to yield of
popped-corn
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CHAPTER 6 CONCLUSION AND RECOMMENDATION
6.0 Based on the analysis done in previous chapter, we conclude that the Cooking Time
factor is the important and significance one.
Figure 1.10 Main Effect Plot of Full Factorial
Based on figure 1.10, the circle one is the wanted number of un-popped corn as it
less. Referring to this figure, lowest amount (weight) of un-popped corn is comes with
the use of ACI II brand, High temperature with 3 minutes cooking times. This is due to
the main effect plot, we can see that by using positive (+) level on brand which is ACI II
(in this study), the CTQ or the result of the un-popped corn is lower than the negative (-)
level. It same goes to the temperature and cooking time factor. The (+) level gives less
amount of un-popped corns compare to the (-) level.
However, as been analyzed before, the only factor that is significance is Time. Hence,
to come out with the same result, (less amount of un-popped corn) but more
economically and saving the cost, we propose to use the (-) of brand, in this study,
TESCO is the one. This is for the reason that the two brands is not significance. Thus,
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pop corn maker can still have the less number of un-popped corns with low branding
kernels but it should come with the high temperature and time.
We come out with regression to predict the amount of un-popped corn. 10 samples
are taken by using TESCO brand and 50gram of kernels. We use High temperature. We
stop the data or experiment once the kernels started to burnt. We repeated the measuring
for 3 times. The table 4.8 shows the average of the data gain from 3 repeating measures.
Exp Num Weight Temperature Time Result
1 50g High 0.5 min 50g
2 50g High 1 min 49.5 g
3 50g High 1.5 min 49.5 g
4 50g High 2.0 min 46.2 g
5 50g High 2.5 min 45 g
6 50g High 3.0 min 34.5 g
7 50g High 3.5 min 34.5 g
8 50g High 4 min 30.0 g
9 50g High 4.5 min 20.7 g
10 50g High 5 min 20.7 g
Mean 38.06
SD 11.60
Table 4.8 Samples for Regression development
We calculate the regression sample by using Minitab 1.5. The result are shown below.
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The R square is equal to 92.6% or 0.926 which shows that the correlation between time
and the CTQ (weight of un-popped corn) is 92.6 %. The R adjusted shows that the
success of the model or formula is 91.6 % or it also can be said that the formula has
accounted for 91.6% of the variance in the criterion variable.
The formula of the regression is
We are 95 % confidence that by using the obtained data as shown in table 4.8, the mean
will be within 30.87 to 45.25. ( Figure 1.13)
Figure 1.13
95% CI =
= 38.06 1.96 (
)
= 38.06 1.96 ( 7.19)
= 30.87. ; 45.25
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