Design of Experiments
- isabelleadora
- Jan 21, 2023
- 4 min read
In week 12, we learnt about Design of Experiments (DOE). In this blog, I will be explaining how I use Full Factorial and Fractional Factorial method to analyse my data using a given case study. DOE will help me in solving the question posed in the case study. Now what exactly is DOE? It is a statistics based approach to design experiments. It is a method which allows us to identify how variables interact with one another with the fewest trials possible.
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:
1. Diameter of bowls to contain the corn, 10 cm and 15 cm
2. Microwaving time, 4 minutes and 6 minutes
3. 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
The data is shown below.
Full Factorial Method
1. Fill up the data given in the excel sheet
2. Use the data from the table (the average HIGH and LOW values of the factor) to plot the graph
Analysis
As shown on the graph, when Factor A decreases from 15cm to 10cm, the mass of the bullets increased from 1.56 g to 1.71 g.
When Factor B decreases from 6 minutes to 4 minutes, the mass of the bullets increased from 1.20 g to 2.08 g.
When Factor C decreases from 6 minutes to 4 minutes, the mass of the bullets increased from 1.20 g to 2.08 g.
We can tell how significant a factor is based on the steepness of the graph. The steeper it is, the more significant it is. From most to least significant:
Factor C - Power
Factor B - Microwaving Time
Factor A - Diameter of Bowl used
Interactions between factors
For A & B:
For B & C:
For A & C:
Analysis
Based on the graphs, only the graph of A & B had an intersection, meaning there is an interaction. As for A & C and B & C, there is no intersection, hence there is no interaction.
Fractional Factorial Method
For Fractional Factorial method, I chose the runs 2, 3, 5 and 8, whereby the high and low levels occur at equal amount of time, giving us good statistical proportions. Follow the same steps as Full Factorial method to get the graph for the effect of the individual factors.
Analysis
Based on the graphs, when Factor A decreases from 15cm to 10cm, the mass of the bullets decreased from 0.95 g to 0.81 g.
When Factor B decreases from 6 minutes to 4 minutes, the mass of the bullets increased from 0.70 g to 1.06 g.
When Factor C decreases from 6 minutes to 4 minutes, the mass of the bullets increased from 0.265 g to 1.50 g. We can tell how significant a factor is based on the steepness of the graph. The steeper it is, the more significant it is. From most to least significant:
Factor C - Power
Factor B - Microwaving Time
Factor A - Diameter of Bowl used
What became drastically different from using Full Factorial Method was Factor A's (Diameter of bowl used) gradient changing from positive to negative. Hence, using Fractional Factorial is not as accurate and reliable as compared to Full Factorial method. Hyperlink to the excel sheet
Reflection
During the tutorial when Dr Noel taught DOE, I was absent as I was sick. When I heard that we had to do the pre-experiment for the practical 2 days later, while the slides were informative on why DOE is important, I was unsure on how to fill up the excel sheet to get the data needed to analyse the data in the first place. I would like to express my gratitude to my groupmate, Alvin, for teaching me how to do it. He definitely helped me understand how to use DOE as he guided me step by step as I streamed. While I was not good at excel and occassionally misclicked or took a while to process, he was patient with me and I would like to thank him for that.
As for DOE itself, I think that it is an efficient way to design experiments. For example, Fractional Factorial method allows us to do an experiment using a few runs and still be able to get sufficient data to analyse. Using both Fractional and Full Factorial method also allows us to analyse the data quickly as we can compare the data using graphs. Furthermore, we can analyse the interaction between the factors which is something useful for our Capstone Project. This allows us to make changes to the factors to make a project more succesful.
The practical was quite memorable and while it was one of the easiest, we encountered a few hiccups. My group decided to take the safe route and only pushed the handle of the catapult 2 clicks back as we wanted to save time and not constantly change where we placed the tray of sand. Dr Noel suggested we push it all the way so we could have fun but Alvin refused to have fun leading to Dr Noel saying he had an unhappy childhood throughout the practical, which was so funny.
One of the hiccups we faced was when the rubber band of one of our catapult came off due to unknown reasons. It took us quite a while to put it back together and we realised that if we fixed it at the end instead of during the time we did our experiment, we could have completed our tasks earlier.
Before ending the day, we had a challenge to hit mini versions of DCHE by changing the settings of our arm length, stop angle and the density of the ball. We used the data we collected throughout the practical to try to get the optimal settings. We did not manage to hit all of them but it was so fun to do so and we celebrated when we did manage to hit one.
All in all, DOE is an important skill for us engineering students and one thing that I need to work on is knowing whether using which method, Full or Fractional Factorial, is more feasible for the experiment.
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