DOE Case Study
Hello
everyone! Welcome back to my 4th blog entry! In this
blog entry, I will be discussing about the topic of Design of Experiment (DOE)
and what I have learnt about it.
This
blog entry contains a full factorial and fractional factorial analysis for a given
case study on ESP Brightspace, followed by a learning reflection of my tutorial
and practical sessions.
FULL FACTORIAL Data Analysis
Effect
of each factor & their rankings
Factor
A: Diameter of bowls to contain the corn, 10 cm and 15 cm
Factor
B: Microwaving time, 4 minutes and 6
minutes
Factor
C: Power setting of microwave, 75% and
100%
The
most impactful factor which affected the number of inedible “bullets” (un-popped
kernels) is factor C, followed by factor B and lastly, factor A.
This
result is obtained from each factor’s gradient on a linear graph. The gradient
of a factor will determine the significance of the factor’s impact on the
result, i.e. a higher magnitude will result in higher significance.
Gradient
of factor A: - 0.15
Gradient
of factor B: - 0.86
Gradient
of factor C: - 2.04
Since
all the gradient values of the factors are negative, we can infer that the high
value of each factor will give more favorable results.
Interaction effects
(A
x B)
At
LOW B,
Low
A average = (0.74 + 3.12) / 2 = 1.93
High
A average = (3.52 + 0.95) / 2 = 2.235
Total
effect of A = 2.235 - 1.93 = 0.305
At
HIGH B,
Low
A average = (2.52 + 0.52) / 2 = 1.52
High
A average = (1.52 + 0.32) / 2 = 0.92
Total
effect of A = 0.92 - 1.52 = - 0.6
Since
one line is +ve and the other is -ve, hence, it can be concluded that there is
a significant interaction between A and B
(A
x C)
At
LOW C,
Average
of LOW A = (2.52 + 3.12) / 2 = 2.82
Average
of HIGH A = (3.52 + 1.52) / 2 = 2.52
Total
effect of A = 2.52 - 2.82 = - 0.3
At
HIGH C,
Average
of LOW A = (0.74 + 0.52) / 2 = 0.63
Average
of HIGH A = (0.95 + 0.52) / 2 = 0.735
Total
effect of A = 0.735 - 0.63 = 0.09 (Increase)
Since
one line is +ve and the other is -ve, hence, it can be concluded that there is
a significant interaction between A and B
(B
x C)
At
LOW C,
Average
of LOW B = (3.52 + 3.12) / 2 = 3.32
Average
of HIGH B = (2.52 + 1.52) / 2 = 2.02
Total
effect of B = 2.02 - 3.32 = - 1.3
(Decrease)
At
HIGH C,
Average
of LOW B = (0.74 + 0.95) / 2 = 0.845
Average
of HIGH B = (0.32 + 0.52) / 2 = 0.42
Total
effect of B = 0.42 - 0.845 = - 0.425 (Decrease)
Since
the lines are parallel, there is NO interaction between B and C.
Here
is the link to the excel sheet : https://docs.google.com/spreadsheets/d/1pJZSI4zVGwYxsA01fbdGIfo59PssN-ql/edit?usp=sharing&ouid=104767778966861281541&rtpof=true&sd=true
In conclusion,
Factor
C (Power setting of the microwave) has the most significant impact on the
number of bullets. Factor B (Microwaving time) has a moderate impact, while
factor A (diameter of the bowl to contain the corn) has the least significant
impact on the number of bullets.
However,
despite the difference of each factor's impact on the number of bullets, it is
concluded that an increase in each factor will result in the decrease of the
number of bullets, and hence the increase of popcorn yield.
Hence,
to achieve an optimal popcorn yield, all the factors should be on the + (HIGH)
side.
In
addition, factors A and B have a significant interaction with each other. This
is the same for factors A and C. However, factors B and C has an interaction of
no significance between them.
FRACTIONAL FACTORIAL Data Analysis
To
start with the fractional factorial data analysis, 4 experimental runs with an
equal number of low and high data for each factor are to be selected.
This makes the data orthogonal and balanced, resulting in good statistical
properties. With that in mind, runs 2, 3, 4, and 5 were selected.
The
most significant factors that affect the number of inedible "bullets"
(un-popped kernels) remaining at the bottom of the bag of popcorn are factor C followed
by factor B and factor A.
This
result is obtained from each factor’s gradient on a linear graph. The gradient
of a factor will determine the significance of the factor’s impact on the
result, i.e. a higher magnitude will result in higher significance.
Gradient
of factor A: 0.36
Gradient
of factor B: - 0.36
Gradient
of factor C: - 1.14
The
gradients of factor A and factor B have the same magnitude, and hence factor A
and factor B has the same significance in affecting the number of bullets.
Since the gradient of factor C is the greatest, factor C has the highest level
of significance.
It
can then be observed the gradients of factor B and C are negative. This tells
us that a high value will result in a lower number of bullets, and hence a
higher yield of edible popcorn.
On
the other hand, the gradient of factor A is positive. This tells us that a high value will result in a higher number of bullets, and hence a lower yield
of edible popcorn.
Here
is the link to the excel sheet: https://docs.google.com/spreadsheets/d/1fMvSLpOpNyhF3FUTUlc3COFAxKt0iZkl/edit#gid=1280236156
In conclusion,
It
can then be observed that an increase in factor B and C will result in a lower number
of bullets, and hence, a higher yield of edible popcorn.
On
the other hand, an increase in factor A will result in a higher number of
bullets, and hence, a lower yield of edible popcorn.
Hence,
to achieve an optimal popcorn yield, factor B and C should be on the high side,
while factor A should be on the low side. This differs from the conclusion of
the full factorial data analysis, where all factors should be on the high side
to achieve a higher yield of edible popcorn.
This
is because fractional factorial data analysis is ‘less than full’. It is more
efficient and resource-effective, but there is a risk of missing information.
Fewer than all possible treatments are chosen to still provide sufficient
information to determine the factor effect.
Learning Reflection
During
the tutorial sessions I had learnt about DOE and the theory behind it. Although
DOE was a new topic, I had already experienced it in one way or another. Since
every experiment done in lab modules had parameters and runs. As such, the
topic was easy to understand.
To
carry out DOE, Microsoft Excel had to be used to input the values, parameters,
and such to create the required graphs and by observing the graphs, information
about the experiment can be obtained. DOE also helps me understand how I can plan
an experiment by varying the parameters to get a accurate result if there are
multiple variables which can vary. I had also learnt about full and fractional
factorial of DOE. Fractional factorial DOE requires less runs and is more cost
and resource efficient but at the cost of accuracy which in certain situations
is more favorable.
Practical
During
the practical session, my peers and I were tasked to carry out an experiment.
This experiment was about using a catapult and ball and noting down the
distance of the ball travelled with the use of 3 different parameters at high
and low values of our choosing. The 3 parameters are the weight of the ball,
the length of the catapult arm, and the stop angle of the catapult arm. We
conducted 8 runs with each run having a mix of low and high parameters.
Each run was replicated 8 times to produce an average value for each run,
increasing the accuracy of the experimental results. After which, we carried
out the steps in DOE to determine the order of the most significant factor in
affecting the experimental results by plotting the required graphs.
After
we had completed this activity, we were informed of a surprise activity where
we had to use the catapult to shoot at targets at varying distances to score points
using the data we had collected. Much to my surprise, the targets are plastics
cut outs with different lecturer’s face on them.
My
group opted to go last as we would have the longest time to strategize and
prepare for the activity. We first started out by noting down the distances of
each lecturer from the starting point and then did test runs on a separate
table to figure out the setting of each parameter to strike each target.
Thanks
to our preparation, we had won! Along with another group we were the first groups
to hit all 4 targets according to our lecturer and we had done so with 2 trial
runs to spare (3 trial runs total and 2 attempts per target).
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