DOE
Hi guys, welcome back to my blog!! For todays blog, I would be covering a case study using Design of Experiment (DOE) and I would also share about my experience during my DOE practical.
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 (low) and 15 cm (high)
Microwaving time, 4 minutes (low) and 6 minutes (high)
Power setting of microwave, 75% (low) and 100% (high)
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 Data Analysis
From this graph, I can conclude that,
- When diameter (factor A) increases from 10cm to 15cm, the weight of the bullets increases from 1.353g to 1.79g
- When microwaving time (factor B) increases from 4mins to 6mins, the weight of the bullets decreases from 1.748g to 1.395g
- When power (factor C) increases from 75% to 100%, the weight of the bullets decreases from 1.955g to 1.1875g.
Therefore, I can conclude that Factor C (power) is the most significant, followed by Factor A (diameter) and lastly Factor B (microwaving time) being the least significant.
Interaction Effects
AxB Interaction
From the interaction between A & B, there is a significant interaction between the 2 as the gradients are different for both (One is +ve while the other is -ve)
AxC Interaction
From the interaction between A & C, there is a small interaction between the 2 as the gradient only differs slightly.
BxC Interaction
From the interaction between B & C, it shows that there is a significant interaction between the 2 as the gradient differs. (One is +ve while the other is -ve)
Therefore, in conclusion, for Full Factorial analysis, the power is the most significant in decreasing the mass of the bullets.
Moving onto Fractional Factorial data analysis
Fractional Factorial data analysis
From the graph, I can conclude that,
- When diameter increases from 10cm to 15cm, the average mass of 'bullets' increases from 0.423g to 1.37g.
- When the microwaving time increases from 4mins to 6mins, the average mass of 'bullets' increases from 0.828g to 0.965g.
- When the power increases from 75% to 100%, the average mass of 'bullets' increases from 0.775g to 1.0175g.
Therefore, I can conclude that Factor C (power) is the most significant, followed by Factor A (diameter) and lastly Factor B (microwaving time) being the least significant.
In conclusion, the results obtained from the Fractional Factorial data analysis is the same as the Full Factorial data analysis, proving that the Fractional Factorial method is more effective and efficient as it is able to produce accurate results using lesser data points.
Learning Reflection
When I was first introduced to DOE, I initially thought it was quite pointless as I felt that there was no need to go through so much trouble just to identify which factor was the most important. However, while Mr Chua was going through the learning package, I realised that my initial thinking was wrong as DOE helps us to make any product that we were making the best version of it by modifying only the important factors. During the tutorial sessions, we also were given a practice question on how to properly apply DOE. The most challenging part was plotting the graph as apart from that, all we had to do was just fill up a table with the given values. However, Mr Chua being the nice person that he is, decided to do a step by step with us, making the graph plotting much easier. Once we got the hang of it, we then had to use this knowledge and apply it to a practical session.
DOE Practical
This practical was by far the most fun practical we had. We had to test the significance of 3 different factors namely arm length, projectile weight and stop angle on the distance travelled by the projectile.
We then had to carry out Full Factorial data analysis. This were the results:
As you can see from this graph, Factor C (stop angle) is the most significant as the difference in distance travelled by the projectile is the largest amongst all the other factors. (136cm travelled with the low angle , 82cm travelled with the high angle). Whereas between Factor A and B, Factor A has a slightly larger impact as the difference between the distances travelled between the high and low value is slightly larger than that of Factor B.
Therefore, Factor C is the most significant factor since it has the steepest gradient, followed by Factor A and lastly Factor B.
Next, we carried out Fractional Factorial data analysis. This was our data:
As you can see from the graph, Factor C (stop angle) is the most significant factor as the difference in distance travelled by the projectile is the largest amongst all the other factors. (96cm when at low angle, 40.8cm when at high angle). Amongst Factor A & B, the difference in Factor A is just slightly larger than that of Factor B. (3.98cm for Factor A, 3.92cm for Factor B)
Therefore, Factor C is the most significant factor since it has the steepest gradient, followed by Factor A and lastly Factor B.
After completing all of this, we had one last challenge and that was to use our data to try and knock down 4 targets placed at different distances with an alternating position. The catapult had to be placed behind a red tape to ensure fairness for all groups. We were given 2 actual attempts for each target and 2 trial attempts. This part of the practical was quite fun as it was a little competitive between each group to see who could knock down the most targets. Although we did not get first, this was definitely the most fun practical I've had throughout CPDD and I can't wait to use what i've learnt in this practical to my other modules!!
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