DESIGN OF EXPERIMENT
Hellloooo, today I will be talking about my experience with the Design of Experiment (DOE) method.
The experiment scenario I was given was to perform the full factorial design and fractional factorial design with 8 replicates to find out which of the factors affects the flying distance.
These are our Factors:
Full Factorial
For the full factorial design, we conducted 64 runs in total for 8 runs with different factors. We follow the image below to see which factor to use.
To give an example, for run 1 it is a minus sign for all factors. Hence we will be using the low arm length (28 cm), low projectile weight (0.88g) and a stop angle of 30° for run 1. It will then be repeated 8 times to normalize the data.
After conducting all 64 runs, these are the results that we got.
Converting these datas into graphs will enable us to measure the effect of each factor and rank them according to their significance.
When arm length increases from 28cm to 33cm, the flying distance of the projectile decreases from 206.66cm to 163.09cm.
When projectile weight increases from 0.88g to 2.08g, the flying distance of the projectile decreases from 194.0cm to 175.75cm.
When the stop angle increases from 30° to 50°, the flying distance of the projectile increases from 160.81cm to 208.9375cm.
Ranking of the factors (From most significant to least significant)
Stop angle (C)
Arm Length (A)
Projectile weight (B)
Hence, The most significant factor is stop angle as it has the steepest gradient out of all 3 factors.
Now, we can determine the interaction effects. Two factors are said to interact with each other if the effect of one factor on the response variable is different at different levels of the other factor.
These are the interaction effect graph for full factorial design:
The lines for this graph all look kinda parallel and do not intersect each other. Hence, there is no interaction.
The gradients of both lines are different by a little margin. Therefore there’s an interaction between A and C, but the interaction is small.
The gradients of both lines are different by a little margin. Therefore there’s an interaction between B and C, but the interaction is small.
This is the link to excel file where all the datas and graph is: https://1drv.ms/x/s!AmP0W9yQmZRHjkYdvDQ32znGd6AP?e=3m6vDl
Fractional Factorial
For the fractional factorial design, we conducted 32 runs in total for 4 runs with different factors. We follow the image below to see which factor to use.
We choose to conduct the fractional factorial run using Run 2,3,5 and 8 as there is an equal mix of Low (-) and High (+) for all 3 factors. Where all factors occur the same number of times which is said to be orthogonal.
This will provide good statistical properties.
After conducting all 32 runs, these are the results that we got.
Converting these datas into graphs will enable us to measure the effect of each factor and rank them according to their significance.
When arm length increases from 28cm to 33cm, the flying distance of projectile decreases from 202.69cm to 163.09cm.
When projectile weight increases from 0.88g to 2.08g, the flying distance of the projectile decreases from 194.06cm to 172.19cm.
When the stop angle increases from 30° to 50°, the flying distance of the projectile increases from 159.50cm to 206.75cm.
Ranking of the factors (From most significant to least significant)
Stop angle (C)
Arm Length (A)
Projectile weight (B)
Hence, The most significant factor is stop angle as it has the steepest gradient out of all 3 factors.
The graph for fractional actually showed the same result as full even though their datas are slightly different.
Now, we can determine the interaction effects. Two factors are said to interact with each other if the effect of one factor on the response variable is different at different levels of the other factor.
The gradients of both lines are negative and different values. Therefore there’s a significant interaction between B and C.
There is interaction between factor A and C. In this graph, both of the lines are not intersecting, however, they will eventually meet since they are not parallel. The gradients of both lines are different.
There is interaction between factor A and C. In this graph, both of the lines are not intersecting, however, they will eventually meet since they are not parallel. The gradients of both lines are different.
This is the link to excel file where all the datas and graph is: https://1drv.ms/x/s!AmP0W9yQmZRHjkYdvDQ32znGd6AP?e=3m6vDl
Personal Reflection
Before doing the practical, I had to attend a tutorial first where the teacher first introduced the concept of Design of Experiments (DOE) to me. I knew this was important to me as this knowledge is probably going to help me in the future such as in my Final Year Project (FYP).
This is not the first time that I had been exposed to DOE, I just did not know that what I was doing last time was actually DOE. In a module I took last year there was a practical where we were investigating the parameters that affect leaching. In that practical, DOE was used to identify the optimal process parameters to extract the highest amount of coffee solubles from roasted coffee beans.
I have learn that DOE is:
A statistics-based approach to designing experiments.
A methodology to obtain knowledge of a complex, multi-
variable process with the fewest trials possible.
An optimisation of the experimental process itself.
The backbone of any product design as well as any process/ product improvement efforts.
I have also learned to do a full factorial design and I can also do a fractional factorial design.
Doing a full factorial design means that I have to do the amount of treatments according to the number of factors I have from the table below.
As can be seen up to 3 factors the amount of treatment is still manageable but afterwards the number treatments start going to double digit and even triple digit. Oh my gosh, when I saw the numbers I was shocked, it just wasn’t realistic to do that many treatments. It’s going to take too much time and manpower and it's just going to make everyone frustrated. Luckily, there is a solution. That is to do fractional factorial design instead.
As the name implies, A fractional factorial is ‘less than full’. Fewer than all possible treatments are chosen to still provide sufficient information to determine the factor effect. It is more efficient and resource-effective, but we do risk missing information. In choosing the factorial design to carry out, we have to choose a Balanced design where all factors occur (both low and high levels) the same number of times. It is then said to be orthogonal and will give Good statistical properties.
I also learned about the interaction effect. Two factors are said to interact with each other if the effect of one factor on the response variable is different at different levels of the other factor.
Now onto the Practical. I really enjoyed it, it was very fun. We had to perform both full and fractional factorial design to find out which of the 3 factors (Arm length, projectile weight or stop angle) affects the flying distance the most. It was fun because we had a ccatpult that we used to launch the projectile for the runs, sometimes it went off course and hit someone. (It was ridiculously funny.🤣🤣🤣)
The most exciting activity however was the second part of the practical where we were given a challenge to hit down 4 targets placed at different lengths on the table. (PS: the target was a laminated paper of our teachers.) We were given few attempts for trial and a few actual attempts. Our group first measured the distance of each target so that we could cross check it with the data that we collected from the previous part of the practical to see if there was any target distance that was close to the data of the flying distance we collected. There was of course, so we followed the level of the factor that matched the distance. I’m happy to say that our group managed to hit all 4 targets!!! We were first place along with another group that also managed to hit down all 4 targets.
Here are some pictures:
The Catapults and the Projectiles
Our group picture after we hit down all 4 targets
Group picture with the other group that also hit down all 4 targets
The 4 targets
CASE STUDY
What could be simpler than making microwave popcorn? Unfortunately, as everyone who has ever made popcorn knows, it’s nearly impossible to get every kernel of corn to pop. Often a considerable number of inedible “bullets” (un-popped kernels) remain at the bottom of the bag. What causes this loss of popcorn yield? In this case study, three factors were identified:
Diameter of bowls to contain the corn, 10 cm and 15 cm
Microwaving time, 4 minutes and 6 minutes
Power setting of microwave, 75% and 100%
8 runs were performed with 100 grams of corn used in every experiments and the measured variable is the amount of “bullets” formed in grams and data collected are shown below:
Factor A= diameter
Factor B= microwaving time
Factor C= power
Full Factorial
Interaction effect
The gradients of both lines are negative, however they are not parallel. The interaction between factor B and C is still considered small as the lines are not intersecting but there is still interaction between both.
Ranking of the factors (From most significant to least significant)
Power setting of microwave (C)
Microwaving time (B)
Diameter of bowls to contain the corn (A)
This goes to show that the factor of Power setting is the most significant factor (due to it having the steepest gradient) that is causing more inedible “bullets” to be formed. Hence, resulting in more loss of popcorn yield.
For this fractional factorial data, it is very similar to the full factorial data with some minor difference but it has the same trends. Factor C, Power of the microwave is still the most significant factor. However, Factor A and B have similar gradient here.
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