Blog 3: Design of Experiments (DOE)
Hello!! everyone welcome back to another blog of my third blog. In this blog, I will be sharing to you what I have done for DOE.
For this blog, I am required to analyze what causes a loss in popcorn yield. Specifically, I will experiment with three factors: diameter, microwaving time, and power, to measure their effect on the number of un-popped kernels, or 'bullets,' that remain at the bottom of the bag. After conducting the experiment, I will perform both a full factorial design and a fractional factorial design for data analysis. The blog will be split into two parts, each focusing on one of these analyses, and I will also reflect on my learning throughout the process. Before diving into the analysis, I will share the data collected from 8 experimental runs where - means low level of each factor while + means high level of each factor.
Table 1: Data from experiment
Run Order | Diameter (A) | Microwaving time (B) | Power (C) | Bullets (grams) |
1 | + | - | - | 3.11 |
2 | - | + | - | 2.11 |
3 | - | - | + | 0.74 |
4 | + | + | - | 1.11 |
5 | + | - | + | 0.95 |
6 | + | + | + | 0.32 |
7 | - | + | + | 0.11 |
8 | - | - | - | 3.12 |
If you want to view the excel file that I used to do the analysis, click on the excel file below.
Part 1: Data analysis of Full Factorial
Determining the effect of single factors and their ranking.
To determine the effect of each individual factor and rank them, I will first calculate the average values for the high and low levels of each factor. Afterward, I will use these values to create a graph, ranking the factors accordingly. I'll provide an explanation for the ranking later. The attached figures show my calculations and the corresponding graphs.
Ranking of factors and reasoning
From Figure 2, I can conclude that power is the most significant factor, followed by microwaving time, and lastly, the diameter. This is evident from the graph, as increasing the microwave power from 75% to 100% led to a reduction in the weight of bullets from 2.36g to 0.53g, resulting in the steepest gradient for power at 1.83, indicating it has the greatest influence on the weight of bullets.
Similarly, increasing the microwaving time from 4 minutes to 6 minutes caused the weight of the bullets to decrease slightly, from 1.98g to 0.9125g, resulting in a less steep gradient of 1.0675, suggesting that microwaving time still has a significant impact, though less than power.
Lastly, increasing the diameter of the bowl from 10 cm to 15 cm led to a smaller decrease in bullet weight, from 1.52g to 1.3725g. The gradient for diameter, at 0.1475, is the least steep, indicating it has the smallest influence on the weight of bullets.
Determining of interaction effects between 2 factors
To determine the interaction effects, I will begin by selecting pairs of factors for comparison, ensuring that all combinations are considered. The factor pairs I will be analyzing are A x B, A x C, and B x C. Similar to how I determined the effect of individual factors, I will first calculate the average values for the high and low levels of each pair. These values will then be used to create a graph to rank the interactions. A detailed analysis of these interactions will follow in the next section.
Factors A and B
From figure 4, the positive gradient at low microwaving time (+0.1) suggests that as the diameter increases, the weight of bullets increases. The negative gradient at high microwaving time (-0.395) indicates that as the diameter increases, the weight of bullets decreases at higher microwaving times. Therefore, it suggests that there is a moderate interaction between diameter and microwaving time.
Factors A and C
From figure 6, The negative gradient at low power (-0.505) suggests that increasing the diameter results in a decrease in the weight of bullets at low power. The positive gradient at high power (+0.21) suggests that increasing the diameter leads to a slight increase in the weight of bullets at high power. Therefore, both gradients are different as there is a positive and negative gradient. Hence, it suggests that there is a significant interaction between the 2 factors.
Factor B x C
From figure 8, both gradients are negative, indicating that increasing the microwaving time reduces the weight of bullets at both low and high power levels. However, the steeper the gradient at low power (-1.505) suggests that microwaving time has a stronger effect on reducing the weight of the bullets when the power is lower. At high power, the gradient is still negative (-0.63), but the effect of microwaving time is less pronounced. Therefore, both gradients are both negative but with a large difference in magnitude (-1.505 vs. -0.63) suggests a moderate interaction between microwaving time and power
Conclusion of findings
In conclusion, the most significant effect is power of the microwave, followed by microwaving time and lastly the diameter of the bowl. This is evident in both main effects and interaction effects. Furthermore, interaction effects also reveals that power is the most significant effect as it has a significant interaction with diameter and moderately interaction with microwaving time. Therefore, if one want to optimize popcorn yield, the microwave power should be the first to adjust, followed by microwaving time, and lastly diameter of the bowl.
Part 2: Data analysis of fractional factorial
Reasoning of selecting 4 experiments from full factorial data
For fractional factorial, I chose runs 1,2,3 and 6 because all factors for all runs are both varied and balanced meaning that all factors occur at both low (-) and high (+) the same number of times. Hence, this makes it statistically orthogonal and have a good statistical properties.
Determining the effect of single factors and their ranking.
To determine the effect of each individual factor and rank them, I will do the same as what I did for full factorial. The attached figures show my calculations and the corresponding graphs.
Ranking of factors and reasoning
From figure 10, I can conclude that power is the most significant factor, followed by microwaving time, and lastly, the diameter. This is evident from the graph, as increasing the microwave power from 75% to 100% led to a reduction in the weight of bullets from 1.31g to 0.265g, resulting in the steepest gradient for power at 1.045, indicating is the most influential factor in reducing the weight of bullets.
Similarly, increasing the microwaving time from 4 minutes to 6 minutes caused the weight of the bullets to decrease slightly, from 0.96g to 0.6075g, resulting in a less steep gradient of 0.3525, suggesting that microwaving time still has a significant impact, though less than power.
Lastly, increasing the diameter of the bowl from 10 cm to 15 cm led to a increase in bullet weight, from 0.713g to 0.8575g. The gradient for diameter, at 0.1445, is the least steep, indicating it has the smallest influence on the weight of bullets.
Conclusion of findings
In conclusion, the rankings remained the same as in full fractional. From the most significant effect of power, followed by microwaving time and lastly diameter. Additionally, to optimize popcorn yield and reduce the weight of bullets, the microwave power must be prioritized, followed by microwaving time, while diameter has minimal effect and may not require significant adjustment.
Part 3: Learning Reflection
After having gone through both the practical and tutorial lessons of design of experiments (DOE), I will be reflecting on what I have learned and applied through my experience. I feel that DOE is an important skill to have as in the future, it can help me provide a structured approach to solving complex problems, especially in engineering fields. If I work in process optimization or research and development as a chemical engineer, the ability to design efficient experiments will help me test multiple variables simultaneously, reduce waste, and achieve cost-effective solutions. Therefore, my reflection will focus on my learning process, challenges and and how this relates to chemical engineering and future work.
During the DOE experiment, I learned how to use full factorial and fractional factorial design to test multiple factors at different levels simultaneously, which is crucial as my group has to determine which effect is the most significant that affected the projectile distance. The tutorials also taught me hoe to analyze the data collected from full and fractional design with a balance experiment with accuracy. Prior to the experiment, I expected that the data analysis to follow for full and fractional factorial to show me the most significant factors influencing the projectile distance. However, upon doing the challenge, we encountered the issue of the catapult not knocking down closer targets, this forced us to improvise and use a partial loading method, something not covered in the lessons. This make me realize that there are also other factors that affect the projectile distance such as the tension of the rubber band on the catapult.
While the tutorials gave me a clear idea of how to identify the optimal combination of factors for maximum distance, the unexpected difficulty of hitting shorter-range targets required us to rethink our approach. In this case, I realize that the interaction between factors wasn't as straightforward as anticipated. As mentioned earlier, the tension of the rubber and connected to the catapult also affected the projectile distance. To overcome this, my group and I have to make on-the-spot adjustments by modifying the loading of the catapult to achieve shorter distances which wasn't the original plan. This taught me that not only must I always expect the unexpected as uncontrolled variable like rubber band tension, I must also be flexible in dealing with unexpected outcomes is equally important.
Reflecting on this experience, I also realized that DOE cannot run all experiments as it will be time consuming and a realistic approach to restrict the number of runs is to use fractional factorial. Although fractional factorial saves time, but doing it will risk the accuracy of results as there is lesser data points for the interactions between factors. Hence, there is a trade-off when doing fractional factorial only.
Moving forward, DOE will be helpful in my upcoming half-boil egg maker project, where I need to test the factors affecting the perfect half boil egg such as time, temperature and size of egg for consistent results. Lastly, I will also have to set aside more time for this project as there will be unforeseen circumstances. Therefore, applying DOE will ensure a systematic, efficient approach to testing variables, ultimately leading to a more reliable and optimized design.
That's it for this this blog, I hope u enjoy reading this blog and see you in the next blog! 😄😄
Comments