Blog 3: Design of Experiments (I've run out of joke titles)
- harrenchd
- Feb 2, 2025
- 6 min read
Updated: Feb 3, 2025
Happy new year everyone! It's been a while since the last blog, hope y'all are doing well :)
Today's blog will be on Design of Experiments (DOE)!
Design of Experiments: An Introduction
But what exactly is that?
The design of experiments, also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. (Found this on Google)
This basically means that it is a method used to determine the significance of factors in an experiment by planning, conducting and analyzing experiments.
In the case of my blog, we are analyzing the factors affecting the popping of popcorn kernels in a microwave; Diameter, Microwaving Time, and Microwave Power!
Here's the full case study:
What could be simpler than making microwave popcorns? Unfortunately, as everyone who has ever made popcorns 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, the following 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
Luckily for me, the experiment values were already given (with XX being the last two digits of my admin number; that is, 15) so all I had to do was figure out what to do with all the numbers.
Analyzing the data:
There are two methods of assessing the data values to decide the most significant factor, and they are the Full Factorial Design and Fractional Factorial Design.
Full Factorial Design:
This method uses ALL combinations of factors to determine the factor significance. This means that the method utilizes all 8 runs to determine which factor affects the number of kernels that have not yet popped.
Determining the effect of single factors and their ranking:
Using all the data from the values above (because this is a FULL factorial design, remember?), I found which factors were most significant in affecting the mass of "bullets" (unpopped kernels). Here's how!
Each factor had to be separated into two parts where each portion is the level of each factor (+ and -), where + is higher (15cm diameter, 6min, 100% power) and - is lower (10cm diameter, 4min, 75% power). I then took the average of each portioned total to find the average mass of "bullets" based on the factor level of each factor. In the end, this is what I came up with.
Tabulated data: | ||
| + | - |
Factor A | 1.3925 | 1.54 |
Factor B | 0.9425 | 1.99 |
Factor C | 0.555 | 2.4375 |
Table of tabulated data
I then subtracted the values from each other to find the difference, which would show the significance of each factor! The values are tabulated in a graph to visually show the difference.
From the graph, we can see the most significant factor by comparing the gradients. In this case, Series1 (which is power because I suck at Excel formatting and I don't know how to fix this) has the largest gradient, followed by Series2 (which is microwaving time) and Series3 (which is diameter). Since the lines all have a gradient, they affect the mass of "bullets" to a certain degree, though the power affects the mass of "bullets" the most.
Hence, the significance of each factor is like so:
Power>Microwave Time>Diameter of Bowl
Determining the interaction effects:
Although the significance of each factor has been determined, there is a possibility that the factors interact with each other, which may alter the end result as well. Let's dive into it!
By adding the factors with each other depending on the factor levels, we can see the interaction between each factor! Here's an example:
Factor AB= Diameter x Microwaving Time
Factor AC= Diameter x Power
Factor BC= Microwaving Time x Power
To find the interaction effects between A and B, we can compare the runs where the factor levels of A and B were differing, that is, whenever they were + and -. This allows us to compare the levels through the gradients when we plot them onto a graph!
Sounds complicated, but I think it's easier if I just show it:
From the graph, we can see that the gradients of the lines are relatively small. This means that the interactions between the diameter and microwave time are apparent, but do not have a large amount of interaction. It does however show that the interactions are positive, in the case that the increase in factor levels do not result in a decrease in popping the kernels.
Compared to the first graph between A and C, we can see the gradient is slightly steeper, meaning that the interaction between the diameter of the bowl and the microwave power is higher than that between the diameter and microwaving time. It also shows that the interaction brings more positive results as having a high power and large diameter results in the lowest mass of unpopped kernels.
Out of all the graphs, this had the largest gradient meaning it had the largest interactive effect. We can see that the difference between the microwave times had lead to a massive change in the final mass of unpopped kernels, and also that the interaction between the microwaving power and time had lead to a positive effect yet again, as using both + factor levels lead to the lowest mass of unpopped kernels.
Conclusion:
This was a lot of runs. From what we have analyzed, we can see that the most significant factor was the power of the microwave. Hence, to minimize the amount of "bullets", we need to have the highest power, the longest microwaving time and a bowl with a larger diameter. Kind of just makes sense in my opinion.
However, doing this in real life would be extremely inefficient as we need to do 64 RUNS which is not good. We waste, resources, time and most importantly, popcorn. This is where the fractional factorial design can come in handy!
Fractional Factorial Design:
On the other hand, Fractional Factorial Design uses a subset of the full factorial design. Although this method is more efficient, there is a chance that important information is left out, such as statistical anomalies. In this case, we are using half the runs, so 4 runs. However, the runs have to be picked in such a way that the factor levels (+ and -) are both varied and balanced so as to ensure all factors occur the same number of times. Hence, I picked the runs 1, 2, 5 and 6!
Determining the effect of single factors and their ranking:
Similarly, using the Fractional Factorial Method, we use the same methodology but just with less steps, since we only have to use four different subsets of factors and their levels.
Again, each factor had to be separated into two parts where each portion is the level of each factor (+ and -), where + is higher (15cm diameter, 6min, 100% power) and - is lower (10cm diameter, 4min, 75% power). I then took the average of each portioned total to find the average mass of "bullets" based on the factor level of each factor. In the end, this is what I came up with.
Also, here's a data table of what I used to make the graph!
Tabulated data: | ||
| + | - |
Factor A | 1.735 | 1.55 |
Factor B | 1.235 | 2.05 |
Factor C | 0.635 | 2.65 |
Again, we are brought back to making the graph. I learnt to label the graph properly for once, which was something cool.
As we can see, the gradient meant the significance that each factor had in changing the final mass of unpopped kernels. This meant that the higher the gradient, the more significant the factor had in popping more popcorn kernels. Again, the power had the most significant effect, followed by the microwaving time and finally the diameter of the bowl.
Conclusion:
Similarly to the Full Fractional Design, the significance followed the same order: Power>Microwave Time>Diameter, surprise surprise! From my own experience, this method has been fairly accurate, especially in the practical where we experimented using this exact method! We launched 3D printed balls using catapults, measured their lengths, competed with other groups and had an amazing time. Then reality kicked in and I had to vacuum the floor. Man.
Final Thoughts:
DOE is a really good method to use when it comes to accessing information in order to improve quality and find out cause-and-effect relationships! It is especially helpful in Chemical Engineering when we want to optimize process lines but don't have a clear method to start with. This was really interesting to learn as it's something I've never learnt before! I wish to never do this again. My brain is not enough to figure this out.
Thanks for reading! Hope to see you in the next blog. In the meantime, have a cookie! 🍪
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