Blog 4 Design of Experiment (DOE)
Waddup everybody😸😸!! It has been some time since I last blogged. So, for this week's blog, I will be covering an interesting topic, Design of Experiment (DOE). Using FULL FACTORIAL and FRACTIONAL FACTORIAL data analysis, I will be trying to solve a Case Study😨.
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: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:
Full Factorial Analysis
The effects of Single Factor are totaled and averaged separately. This is shown on the graph below.
These data of + (HIGH) and - (LOW) were then used to plot a scatter which will allow us to see which factor is the most significant by looking at how steep the gradient is. The graph is shown below.
From the graph above, we can infer that - When the diameter increases from 10cm to 15cm, the mass of "bullets" decreases from 1.58g to 1.43g.
- When the microwaving time increases from 4minutes to 6minutes, the mass of "bullets" decreases from 2.01g to 1.00g.
- When the power setting of the microwave increases from 75% to 100% , the mass of "bullets" decreases from 2.45g to 0.56g.
From these values, we can conclude that
Interaction Effect
The purpose of studying the interaction effect is to find out whether the effect of one variable depends on the value of another variable. For example, checking whether the effect of microwaving time at high microwave power is different as low microwave power. A x B
The gradient of both lines are different. Therefore, there is a significant interaction between A (Diameter) and B (Microwaving Time).
A x C
The gradient of both lines are different. Therefore, there is a significant interaction between A (Diameter) and C (Microwave Power).
B x C
The gradient of both lines are different. Therefore, there is a significant interaction between B (Microwaving Time) and C (Power Setting).
In conclusion, for Full Factorial data analysis, the power setting of the microwave plays the most significant role in decreasing the mass of "bullets" followed by microwaving time and lastly, diameter.Hence, to increase the yield of popcorn, I would use Run 7 which is - Factor A: Diameter of 10cm (-)
- Factor B: 6 Minutes of microwaving time (+)
- Factor C: 100% Power setting of the microwave (+)
This results in the lowest mass of "bullets" (0.23g) which is what we are experimenting for. However, my choice contradicts with the graph plotted as using a higher diameter will help reduce the mass of "bullets" but I chose the run with lower diameter. This is because the data is not valid as we are tasked to use our last 2 digits of our admission number so the data is fabricated and not real. Theoretically, we should use Run 8 as it has higher diameter, higher microwaving time and higher microwave power.
From the graph above, we can infer that
- When the diameter increases from 10cm to 15cm, the mass of "bullets" decreases from 1.58g to 1.43g.
- When the microwaving time increases from 4minutes to 6minutes, the mass of "bullets" decreases from 2.01g to 1.00g.
- When the power setting of the microwave increases from 75% to 100% , the mass of "bullets" decreases from 2.45g to 0.56g.
From these values, we can conclude that
Interaction Effect
The purpose of studying the interaction effect is to find out whether the effect of one variable depends on the value of another variable. For example, checking whether the effect of microwaving time at high microwave power is different as low microwave power.
A x B
The gradient of both lines are different. Therefore, there is a significant interaction between A (Diameter) and B (Microwaving Time).
A x C
The gradient of both lines are different. Therefore, there is a significant interaction between A (Diameter) and C (Microwave Power).
B x C
The gradient of both lines are different. Therefore, there is a significant interaction between B (Microwaving Time) and C (Power Setting).
Hence, to increase the yield of popcorn, I would use Run 7 which is
- Factor A: Diameter of 10cm (-)
- Factor B: 6 Minutes of microwaving time (+)
- Factor C: 100% Power setting of the microwave (+)
This results in the lowest mass of "bullets" (0.23g) which is what we are experimenting for. However, my choice contradicts with the graph plotted as using a higher diameter will help reduce the mass of "bullets" but I chose the run with lower diameter. This is because the data is not valid as we are tasked to use our last 2 digits of our admission number so the data is fabricated and not real. Theoretically, we should use Run 8 as it has higher diameter, higher microwaving time and higher microwave power.
Fractional Factorial Analysis
From the graph above, we can infer that - When the diameter increases from 10cm to 15cm, the mass of "bullets" increases from 1.49g to 1.78g.
- When the microwaving time increases from 4minutes to 6minutes, the mass of "bullets" decreases from 1.99g to 1.275g.
- When the power setting of the microwave increases from 75% to 100% , the mass of "bullets" decreases from 2.73g to 0.53g.
From these values, we can conclude that
Excel Link: Fractional Factorial Analysis
In conclusion, the data for fractional factorial analysis is slightly weird as when the diameter of the bowl increases, the mass of bullets increases which theoretically does not make sense as higher diameter gives a higher surface area so that more corn can become popcorn so the mass of the "bullets" should decrease instead.
From the graph above, we can infer that
- When the diameter increases from 10cm to 15cm, the mass of "bullets" increases from 1.49g to 1.78g.
- When the microwaving time increases from 4minutes to 6minutes, the mass of "bullets" decreases from 1.99g to 1.275g.
- When the power setting of the microwave increases from 75% to 100% , the mass of "bullets" decreases from 2.73g to 0.53g.
From these values, we can conclude that
Excel Link: Fractional Factorial Analysis
In conclusion, the data for fractional factorial analysis is slightly weird as when the diameter of the bowl increases, the mass of bullets increases which theoretically does not make sense as higher diameter gives a higher surface area so that more corn can become popcorn so the mass of the "bullets" should decrease instead.
Learning Reflection
So, for design of experiment tutorial and practical, I actually enjoyed and learn a lot. For the tutorial lesson, I learnt that in the industry, it is infeasible to run all treatment as the more factors we have the more runs we had to do. Thus, it is more realistic to restrict the number of runs. This is known as fractional factorial data analysis. However, although it is more effective and resource-effective, we risk missing information. A good fractional factorial data analysis consists of the equal amount of low and high level. After learning all these, I managed to finished my pre-experiment quickly. With the help of my lecturer, Mr Chua, I also learnt how to plot the graph on Excel.
For the practical lesson, I would like to thank my beloved teammate, Md. Aminur Rahman for creating an excel sheet with the graph. We just have to simply key in the values during our experiment and the graph will appear. I was also surprised that when the length of the arm of the catapult increases, the flying distance decreased. I thought its the other way round where when the length of the arm of the catapult increases, the flying distance will increase due to higher moments. During the group competition, we were lucky that some of the distance from the starting line to the target were similar to our excel sheet so we just had to follow the run number. For the ones that are different, we used trial and error. I also like to thank Jun Kai for his steady hands which successfully hit down all 4 targets which led us to receive the full 10 marks.
All in all, design of experiment is really interesting and fun. I learnt a lot. This is my favourite practical. I am sure that in the future when I am working, I will definitely need to use it.
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