Blog 3: DOE🐶

Welcome back!!!

My last blog was almost 2 and a half months ago.😭😭😭

As such I think for this blog I will take it slow and not yap as much. So without further ado Lettuce🥬 begin.

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What is Design of Experiments (DOE)

DOE is a powerful methodology that helps us understand complex, multi-variable processes by conducting the fewest number of trials possible. In other words, it’s all about optimizing the experimental process itself!

It allows us to explore🔍 the effects of individual factors and how they interact with each other.

In this blog, I’ll focus on two key designs for DOE:

• Full Factorial Design

• Fractional Factorial Design

  
  

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Case Study: Saving Your Teeth🦷 from Popcorn 🍿"Bullets"

Picture this:

You're at the movies 🎥, all hyped up for Emilia Pérez! You grab your snacks, sink into your seat, and take a big handful of warm, buttery popcorn. Life is good. Until…

CRUNCH! 😱

Your teeth just met the ultimate movie-night villain—an unpopped kernel! 🌽💣 OOF. Not the kind of plot twist you were expecting! 😖

A normal person might just sigh, accept their fate, and move on. But you? You’re not normal—you’re abnormal! Instead of letting a rogue kernel ruin your night, you turn this crisis into an engineering⚙️ case study! 🧠

With Design of Experiments (DOE), we can run tests to uncover why some kernels refuse to pop and find the best way to minimize these pesky "bullets." 😅🍿💡

Because let’s be real—movie nights should be about cinematic thrills, not dental drills! 🦷😂

Now to start DOE we will need to determine the factors will will be investigating which are

A: Diameter of bowl🍵 (10cm and 15cm)

B: Microwaving time⌚ (4min and 6min)

C: Power setting of microwave ♨️ (75% and 100%)

We will also need to determine the number of runs we will need to perform for Full Factorial Design. Below is the formula to it.

Below is the table for the 8 runs from the case study

Run Order	A	B	C	Bullets (grams)
1	+	−	−	3.18
2	−	+	−	2.18
3	−	−	+	0.74
4	+	+	−	1.18
5	+	−	+	0.95
6	+	+	+	0.32
7	−	+	+	0.18
8	−	−	−	3.12

Table 1:Amount of bullets for each run (Full Factorial)

From the table above we can calculate the diffrence between the highs and lows of a factor and the effect it has on the amount of bullets form.

To analyze the effect of each factor on the amount of bullets, we calculate the difference between the high (+) and low (-) settings for each factor. By plotting these values on a graph, we can observe their impact based on the slope (gradient) of the trend lines.

From the graph above you can see that the effect with the most impact on amount of bullet produced is the power setting as it has the highest gradient when compared to the other factors. The factor with the next highest impact is the diameter of bowl and finally the effeact with the least amount of impact is the microwaving time.

now we need to find the interactions between the factors. This can be achived by calculating the effect of A at low and high levels of B, which will then be pot on a graph.

From the graph above the gradient of the two lines have different gradients and both are negative, As such there is significant interaction between factors A and B

From the graph above the gradient of the two lines have different gradients however one is positive while the other is negative, As such there is significant interaction between factors A and C.

From the graph above the gradient of the two lines have different gradients and both are negative, As such there is significant interaction between factors B and C

Final Verdict: The Best Popcorn Strategy

From the results, to achieve the least amount of "bullets" in your popcorn bowl:

✅ Use a larger bowl (15 cm)

✅ Set the microwave power to 100%

✅ Microwave for a longer time (6 min)

So next time you're gearing up for a movie night, use engineering to make sure your popcorn is perfectly popped—because nobody wants a dental disaster mid-movie! 🎬

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Fractional Factorial design

Now let's say you wanted to do DOE; however, you don't have enough resources to do 8 runs. Fret not, as there is another method of doing DOE, which is Fractional Factorial Design. It requires fewer runs, and as such, it can use a fraction of the resources that Full Factorial design will need. The runs we will need will be selected on statistical orthogonality. now I cant explain it well but my good friend ChatGPT can.

Statistical orthogonality in DOE means each factor stays independent 🎯, so their effects don’t mix or interfere! 🔬📊 This keeps results clear and unbiased ✅, making it easy to see which factor actually affects the outcome. If factors aren’t orthogonal, their effects get tangled 🤯, like a messy playlist 🎶, making it harder to know what’s really driving the change. So, for the best experiments, keep factors orthogonal and interference-free! 🚀✨

Below is the table for Fractional Factorial design runs

Run Order	A	B	C	Bullets (grams)
1	+	−	−	3.18
2	−	+	−	2.18
3	−	−	+	0.74
6	+	+	+	0.32

From the table above, we can determine the difference between the highs and lows of a factor and its impact on the number of bullet forms.

From the data above we can plot the graph below

As we did previously, we can evaluate the influence of each factor on the number of bullets produced by comparing the gradients.

The factor with the greatest impact remains the power setting, followed by microwave time, and finally, the factor with the least impact is the diameter of the bowl.

This conclusion differs from the one obtained with the Full Factorial design because the Fractional Factorial design, although more cost-effective and requiring fewer resources, may overlook some factors due to it not having the same amount of data to work from than Full Factorial design.

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Learning Reflection: Struggles with DOE 😵‍💫

I’ll be honest—I DON’T UNDERSTAND DOE!!! 🤯

I get that we need a structured way to identify which factors impact an experiment’s outcome, but what I don’t fully understand is why we need to test factors only at high (+) and low (-) levels. Wouldn’t it be better to test a wider range of values instead of just two extremes? 🤔

Another thing I find confusing is how interactions between factors are analyzed. I see the calculations and graphs, but I still don’t fully grasp how to interpret them. It feels like a lot of numbers and gradients, but I struggle to connect them to real-world applications. 📊🔍

I think I need to see more real-life examples or work through hands-on problems to fully understand why DOE is structured this way. Hopefully, with more practice, I can make sense of how these factor levels and interactions actually help improve experimental results! 🚀

That being said, I actually enjoyed the hands-on practical! Even though I don’t fully grasp how DOE works yet, I still had fun recording data and optimizing the catapult settings. 🏹✨ Seeing the results change with different factor levels made the experiment engaging, and I hope with more practice, I’ll finally have my DOE "Aha!" moment! 🚀

Overall, I do see the value of learning DOE. When I enter the workforce, this knowledge will definitely be useful in designing experiments and improving processes for my company. So even though it’s confusing now, I know it’ll pay off in the future! 💡💼

Anyways that's all from me. Adios Amigo