🏮🥳Happy Chinese year year everyone!🎉 This time round I will be sharing about my experience with the amazing design of experiment concept. Through studying it, it appears to be extremely useful to adjust and perfect a theory. You may be wondering what on earth is design of experiment. To put it in simple terms its is somewhat a statical data tabulation chart for us to run test and find the trend of each variable. This is similar to trial and error in mathematics but instead of having only one variable, we can add many variable by using the DOE method!
YES it all sounds super useful and indeed it is. So lets stop talking and start doing!
In this blog I will walk you through the process of how to use DOE and show you a little example.
In a DOE, we have different factors, each factor will have two settings.
+ will be the higher/larger setting
- will be the lower/smaller setting
The example that I will be testing will be on poppy corns🍿
Whenever we microwave popcorns there will always be leftover and unpopped kernels which is really frustrating to bite into so we will use three factors to adjust to have the least unpopped kernel leftovers.
Our three factors will be:
Factor A: Diameter of bowl to contain the corn🥣
Factor B: Microwaving duration ⌛️
Factor B: Microwaving duration ⌛️
Factor C: Power setting for microwave 📺
So previously mentioned, there are + and - in each factor and our settings will be shown below.
Full Factorial
These are the data given to us🧑💻
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After the datas are inserted into the DOE table we are able to plot a graph as shown above.
A short explanation of the graph above is:
When the diameter of the bowl used (factor A) increases from 10cm to 15cm, the average mass of corn bullets decreases from1.88g to 1.77g.
When the microwave time is (factor B) increases from 4 minutes to 6 minutes, the average mass of corn bullets decreases from 2.18g to 1.46g.
When the power setting of microwave (factor C) increase from75% to 100%, the average mass of corn bullets decreases from 2.96g to 0.687g.
Using the graph we can also deduce the factor with the most significant impact and the least significant impact. This is inferred from the gradient of each factor of the linear graphs. The higher the magnitude of the gradient, ie the absolute value, the higher the significance/impact. This can be visualized by the steepest of the graph as well.
Interactions:
Interaction (A x B)
At LOW B,
Average of low A= (0.7+3.1)/2=1.9
Average of high A= (3.9+1)/2= 2.45
Total effect of A= (2.45-1.9)= 0.55
At HIGH B,
Average of low A= (2.9+0.7)/2=1.8
Average of high A= (1.9+0.3)/2= 1.1
Total effect of A= (1.1-1.8)= -0.7
From graph above we can deduce that there is a significant interaction between the diameter (Factor A) and the microwaving duration (Factor B). This is show by the two different lines with - (LOW) B being positive gradient and + (HIGH) B being negative gradient.
Interaction (A x C)
At LOW C,
Average of low A= (2.9+3.1)/2= 3
Average of high A= (3.9+1.9)/2= 2.9
Total effect of A= (2.9-3)= -0.1
At HIGH C,
Average of low A= (0.7+0.7)/2= 0.7
Average of high A= (1+0.3)/2= 0.65
Total effect of A= (0.65-0.7)= -0.05
At LOW C,
Average of low B= (3.9+3.1)/2= 3.5
Average of high B= (2.9+1.9)/2= 2.4
Total effect of B= (2.4-3.5)= -1.1
At LOW C,
Average of low B= (0.7+1)/2= 0.85
Average of high B= (0.3+0.7)/2= 0.5
Total effect of B= (0.5-0.85)= -0.35
The gradient of both lines are negative as seen in the graph above, however they are far from being parallel to each other. Comparing (A x C), (B x C) has a larger interaction as there is a bigger difference in gradient. However, the interaction is considered small when compared to (A x B) as the lines in (B x C) will meet in due course.
This is the link to the excel spreadsheet:
In a nutshell, we can conclude that in the full factorial analysis, the factor with the most significant impact on the unpopped corn bullets start with the power setting of the microwave (factor C), then followed by the microwaving time (factor B) and finally the diameter of bowl used (factor A).
From the interactions, we can see that the power setting on the microwave (factor C) is post the most significant effect on the bullets and it has the least interaction with the two other factors. In addition, microwave duration (factor B) and diameter (factor A) has significant interaction with each other.
Besides having different magnitude of impacts when using the three factors, we can reckon that an increase in each factor will result is a decrease in unpopped corn bullets, which results in a higher popcorn yield. Therefore to achieve maximum yield, all factors should be set to + (HIGH) setting.
Fractional Factorial
🌟I have chosen the 1st, 3rd 4th and 7th run as it is the most well balanced design for the factors. This due to the fact that all factors occur the same number of times ( the high and low) and there it is orthogonal.
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This is the link to the excel spreadsheet:
A short explanation of the graph above would be:
When the diameter of the bowl used (factor A) increases from 10cm to 15cm, the average mass of corn bullets decreases from 0.41g to 1.45g.
When the microwave time is (factor B) increases from 4 minutes to 6 minutes, the average mass of corn bullets decreases from 1.16g to 0.7g.
When the power setting of microwave (factor C) increase from75% to 100%, the average mass of corn bullets decreases from 1.45g to 0.41g.
In the fractional factorial analysis we can see that the factors with the most significant impact on the unpopped corn bullets is both the power setting of the microwave (factor C) and the diameter of bowl used (factor A). This is followed by the microwaving time (factor B) which is the least effective.
It is seen from the graph that factor B and factor C will result in a lesser unpopped corn bullets, and hence a higher yield of edible popcorn.
On the contrary, factor A will leave more unpopped corn bullets and therefore a lower yield of edible popcorn.
So, to achieve maximum yield of popcorn, factor B and factor C should be set on + (HIGH) setting, and the factor A should be set on - (LOW) setting. This poses a contradiction to the full factorial graph in the above as it was decided that all factor should be set to + (HIGH) for maximum yield.
This is mainly due to this analysis being a fractional factorial, which also means that the data is "less than full". This method is usually used when there is a restriction or limitation on time or budget. It is definitely more resource efficient but the downside is that there may be in equality and missing information in the data analyzed hence resulting in another conclusion.
🧠Personal learning reflection🤔💭
Tutorial sessions📖:
Through these tutorial sessions I learnt and understood the meaning and the use of Design of experiment (DOE). After really understanding the principle of DOE I realise how applicable it is in our daily life. I am very sure many people including myself have unknowingly used this before. From what I can recall, in my LPS journey in year 1 I had an experiment on leaching which is a important technique in chemical industry. We were required to find out how to get the highest concentration of coffee with the change of different variables/parameter. They were stirring speed, temperature of water and duration of coffee in hot water. Looking back, that experiment is extremely similar to the one we had in this DOE practical. The similarities are uncanny, however there was one big difference which was the use of DOE. There were definitely more cases of similar experiments especially in my chemical engineering core modules but without much use of DOE.
At first in class it seemed slight confusing at the interaction part of the factors, like how does a non-living thing interact?? However after doing more exposure Mr Chua was able illustrate and verbalize the effect and interaction between each factor. I was essentially the effects on another factor when one factor is used.
The plotting of graph in excel and understanding of data was manageable as our amazing teacher has showed us how to do so. The steps were easy to digest and most importantly easy to understand. These steps are used in both the full and fractional factorial which made it even more useful.
Speaking of full and fractional factorial, they are also undeniably commonly used before learning about them. Although there were new terminologies, the reason users switch from full to fractional factorial is due to limited resources or time which happens regularly in the real world. I learnt about the correct way of choosing data and the reasoning behind them were that there should always be a balance in the - (LOW) and + (HIGH) settings such that they are considered orthogonal. This ensures a balanced analysis of the data even when there is limitations and fractional factorial is used which I absolutely agree with.
With that I believe the tutorial sessions has been very impactful for me as I am able to understand the rationale behind DOE and I am absolutely sure it will benefit and fine tune my future work in CA2 or even capstone!
Practical session👐:
After the tutorial session we had to put to the test what we have learnt in to a practical session! My group and I had an experiment on catapults.
It was honestly extremely fun as I have always wanted to launch one after playing many video games and launching them into sand pits were awesome but it gets better! Before that our task was to find out the significance of each factor we used. We had three factors put into practice, first was the weight of the ball, second the length of the catapult arm and lastly the angle of release for the catapult. We had to conduct 8 runs with each one having a mix of - (LOW) and + (HIGH) setting of each parameter. We then had to replicate each run 8 time for consistency and accuracy hence full factorial took 64 runs💀. Luckily it was still a blast as my group had extreme fun that we forgot to take any video or pictures except one. After the runs we had to plot some graph to see the significance of each factor and find the trends.
As mentioned above we have only on picture and it is shown below.
Next to her with the cyan arrow we have Shaira. She is the ball catcher and her sole purpose is to of course catch all the balls and repeat. I am the one under the purple arrow, I was in-charge of measuring the distance of each ball travelled. However, I actually really wanted to launch the catapult but ladies first... Beside me under the orange arrow we have Diana and beside her is Qian Yu in the yellow arrow as a yellow person. They were the ruthless catapult launchers aiming to destroy me and Shaira by always launching the balls at our face.
Despite getting obliterated, we had much fun and speedily completed our task.
After the completing the excel Mr Chua had a challenge for the class! We had four targets to shoot down and it was very exciting as they were our module teachers:) We had to measure the different distance they were placed in and according to the data and trend we have tabulated we were to shoot them down with very limited attempts. My group was second to go and we did not have much to refer to and devise a plan so we only managed to hit 2 out of 4 of the targets with the given attempts.
I was pretty upset as after us the two other groups had devised a plan by observing my group and manage to shoot down all four targets. I strongly believe that if we had chance to observe and learn from others, we would definitely yield better results. However thinking back there was something I realized. By using our data in the excel sheet we have created ourselves, we were still unable to hit some targets and had to do some manual adjusting and to succeed, we needed to observe others and devise a plan. Does this mean that our data collected was corrupted and wrong? I pondered over it but found out this was due to the fact that those are somewhat inconsistent due to the fact that it is in real life. The values and result will also change as there are way more factors we had not consider such as build material and its consistency, the wind speed and other external factors.
In a nutshell, I have been enlightened with the consistency of the data and the ease of trend and significance finding has been made easier with the help of doe, however in the real world there will be instances where data must be calculated to maximum precision for certain reasons. I wonder how effective will DOE be and will there be any other methods that are better or would supplement the trend and significance finding?
Thanks for sticking around to the end, I hope you thoroughly enjoyed this blog and i'll see you guys in the next one Sayonara👋!
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