BLOG 4 ( DOE )

In this blog, I will be sharing about DOE, which refers to Design of Experiments. So, what exactly does DOE means?

Simply put, DOE is a statistics based approach to designing experiments. It is a methodology to obtain knowledge of a complex, multi-variable process with the least trials as possible. DOE really helps the user to understand step by step of what is happening and how something affects another. With that said, let me share with you how I would go about and carry out DOE on what causes the loss of yield of popcorn.

Realistically, it is impossible to get every kernel of corn to pop when trying to make popcorn. Most of the time, some inedible bullets tend to remain at the bottom. Therefore, through this Case Study, I would be exploring how three different factors actually affect the yield of popcorn.

These Factors include:

1. Diameter of bowls to contain the corn, 10 cm and 15 cm (Factor A)

2. Microwaving time, 4 minutes and 6 minutes (Factor B)

3. Power setting of microwave, 75% and 100% (Factor C)

8 runs were performed with a constant amount of 100 g of corn being used in each experiment. The measured variable will be the amount of bullets being formed in grams.

Full Factorial Method

First, we can do the Full Factorial data analysis. This is the table of data:

​Run Order	A	B	C	Bullets (Grams)
1	+	-	-	3.06
2	-	+	-	2.06
3	-	-	+	0.74
4	+	+	-	1.06
5	+	-	+	0.95
6	+	+	+	0.32
7	-	+	+	0.06
8	-	-	-	3.12

Based on this data, we can get the HIGHS and LOWS of each factor and the average is found to be plotted on a graph.

Using the average values found, we can plot the graph. This graph will show the gradient of each graph which shows how each factor affects the yield more accurately.

When A (Diameter of Bowl) increases from 10cm to 15cm, the average mass of bullets decreases from 1.495 to 1.3475 g.

When B (Microwaving Time) increases from 4 minutes to 6 minutes, the average mass of bullets decrease from 1.9675 to 0.875 g.

When C (Power Setting) increases from 75% to 100%, the average mass of bullets decrease from 2.325 to 0.5175 g.

From this, we can see that Factor C (Power Setting) is the most important factor, followed by Factor B (Microwaving Time) and the least important factor is Factor A (Diameter of Bowl). This can also be noted from the gradients of the 3 graphs, where the gradient of Factor C is the steepest whereas the gradient of A is the most gentle.

Interaction Effects

Next, we will be studying the various interaction effects among the 3 factors. We will be analyzing how one factor will be affecting and causing a difference in the other factors seperately. We can again plot a graph to get a clearer picture of how one factor affects the other.

A x B

The gradient of both lines are different (One is positive while the other one is negative). Therefore, there is a significant interaction between Factor A (Diameter of Bowl) and Factor B (Microwaving Time)

A x C

Since the gradient of the two lines are different, (One is positive while the other one is negative) there is a significant interaction between Factor A (Diameter of Bowl) and Factor C (Power Setting).

B x C

The gradient of both lines are different. However, both of them are negative. The graph for "Low B" is more steep than the graph for "High B". Thus, there is interaction between B and C.

Conclusion

Factor C (Power Setting) is most significant factor, followed by Factor B (Microwaving time) and Factor A (Diameter of Bowl). This can be seen from the graph of A x B x C. Furthermore, for the interaction effects of factor A x B, the change in gradient is not as significant as compared to B x C, which also indicates that A is a less important factor as compared to C. Overall, all of the factors affect each other, but the more significant factors, B and C play a bigger part in affecting the amount of bullets being produced and affecting the final yield.

Case Study Full Factorial.xlsx

Download XLSX • 29KB

Fractional Factorial Method

For the fractional factorial method I decided to use runs 1, 2, 3 and 6. I chose there fractional factorial methods as they would each have 2 high and low for the respective criteria we have. These runs would allow for a better comparison of the factors.

Based on the data above, we can determine the average values of each factor to plot on the graph for comparison.

When A (Diameter of Bowl) increases from 10 to 15 cm, the average mass of bullets increase from 1.4g to 1.69g.

When B (Microwaving Time) increases from 4 to 6 minutes, the average mass of bullets decrease from 1.9g to 1.19g.

When C (Power Setting) increases from 75 to 100%, the average mass of bullets decrease from 2.56 to 0.53g.

Based on the graph plotted, we can deduce that factor C is the most significant factor as it has the steepest gradient. Factor A is the least significant factor as it has the most gentle gradient. Hence factor C is the most significant, followed by factor B, and finally factor A.

Conclusion

Based on the data, we can deduce that factor C is still the most significant factor. This was the same for the Full factorial method. Therefore, the data that is obtained from the factorial method is enough and reliable since both the methods show that factor C is the most significant. However in Full factorial method, the gradient for A is negative as it decreases from Low to High. Whereas in the Fractional factorial method, the gradient for A is positive as it increases from Low to High. This also suggests that there are slight discrepancies that can be seen from using the Fractional factorial method compared to the Full factorial method.

Case Study Fractional Factorial.xlsx

Download XLSX • 16KB

Reflection

When we were first being taught about DOE, it seemed difficult to me. However, as Mr Chua went through with the class, I realized that I had always using DOE when it comes to making a choice for one factor in my previous practical sessions. DOE is used to help us decide which factor to be used when doing an experiment and how to test each factor based on the criteria. I only realized how useful the DOE was when I was doing the practical session.

I went in to the practical thinking that DOE was just used to help us sort our data out when doing the testing of the catapult. I only realized that it was used to help us understand how each factor affect our result differently. It made me understand easily which factor is better and how I should tweak that factor to obtain maximal results. During the practical itself, we had to do so many runs just to get the average for the data which felt pointless at the beginning. However, as I continued through doing the practical, I realized how important each run was as some of the runs were completely different from the other runs. This made us ponder why and we were stuck for some of the runs as the values did not make sense. We realized later that these anomaly runs help to ensure that the data we collect are more accurate, as it was a reflection of actual testing. Therefore, I understood the important of doing multiple tests to get average results through this DOE practical.

The use of DOE would also be useful for me in product design as we eventually also have to test our prototype to see if it actually works and check which factor is the most significant one. DOE is a great technique but it also comes with its flaws as doing the Full factorial run may take very long. Whereas, doing the Fractional factorial is less time consuming but it also leads to some inaccurate data as compared to the Full factorial method. Nonetheless, I am glad that I managed to learn about this new technique and I am intrigued to use it in any future projects where applicable.