Design of Experiment (DOE)

 Case Study

When popcorn is made, there often remain corn kernels which are unpopped, even if the majority of the rest of the corn kernels have popped. To find out what factor causes the most impact on the loss of popcorn yield, three factors were identified:

• Diameter of bowls to contain the corn, 10 cm and 15 cm
• Microwaving time, 4 minutes and 6 minutes
• Power setting of microwave, 75% and 100%

8 runs were performed with 100 grams of corn used in every experiment, 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

Run order	A	B	C	Bullets (grams)
1	+	–	–	3.68
2	-	+	–	2.68
3	–	-	+	0.74
4	+	+	-	1.68
5	+	–	+	0.95
6	+	+	+	0.32
7	–	+	+	0.68
8	–	-	-	3.12

Full Factorial

From the graph, it can be seen that Factor C, the power, has the largest impact on the number of bullets formed. Factor B, the microwaving time, has the second largest impact on the number of bullets formed, and Factor A, the diameter of the bowl, has the least impact on the number of bullets formed.

C > B > A

Interaction Effects

A x B interaction

From the graph, it can be seen that Low B has a positive gradient while High B has a negative gradient, and thus, there is a significant interaction between Factor A and B.

B x C Interaction

From the graph, it can be seen that Low C has a negative gradient, and High C also has a negative gradient. As the gradients differ by a small margin, and thus, there is little to no interaction between Factor B and C.

A x C Interaction

From the graph, it can be seen that Low C has a negative gradient, and High C also has a negative gradient. As the gradients differ by a small margin, and thus, there is little to no interaction between Factor A and C.

In conclusion, for full factorial, Factor C, the power setting, has the most significance, followed by Factor B, the microwaving time, and finally, Factor A, the diameter of the bowl used to contain the corn.

The most significant interaction can be seen between Factor A and B. When the factors are compared, Low B and High B have a positive gradient and a negative gradient respectively.

Fractional Factorial

Before performing fractional factorial, I had to choose which 4 runs I would be using in the analysis. For this activity, I chose runs 1, 2, 5, and 7, as they would have the same number of factors that are high and low, being 2.

From the graph, it can be seen that Factor C has the most steep gradient, and thus, it has the largest and most significant impact on the number of bullets produced. Factor A and B both have the same gradient and thus they both have a less impact on the number of bullets than Factor C.

Here is the link to the google drive containing the excel files that I made use of to come to these conclusions: https://drive.google.com/drive/folders/1WxAwjiRKXlnee8xsur5l4YXFrDhoDezk?usp=sharing

Initially, I didn't think that this process of selecting the runs, collating the data and creating the graphs was all that useful, but after doing this process to find out which factor has the most significance, I realised how powerful this process was, as it also allowed for the interaction between factors to be visualised and graphed out, and I will definitely be making use of it in my future projects.

Practical

Before we did this practical, we had heard about what we would be doing from our lecturer, and I was looking forward to it, as it sounded quite interesting. For the practical, we were tasked with making use of both full factorial and fractional factorial design to determine which factors would affect the distance travelled by a ball using a catapult the most. We were given 2 different arm lengths, 2 types of ball and had to adjust the stop angle of the catapult to 2 different positions.

Two different arm lengths

Two different ball weights

Two different stop angles (I didn't take one but imagine that its 90 degrees)

Here's a table of the different factors that we made use of:

Next, we made use of the full factorial and fractional factorial methods to determine which factor made the biggest impact on the distance travelled by the ball. As we were given 2 catapults, we split our group into 2 sub-groups, with one group performing the fractional factorial design, and my group, doing the full factorial design. After we tabulated the results, here were our findings:

Full Factorial Design results

Fractional Factorial Design results

After we obtained these results, we used the data to plot a graph of the value of the factor against the distance travelled by the ball, in order to determine which factor had the most impact on the distance travelled. Here are our graphs:

Full Factorial Design Graph

Fractional Factorial Design Graph

Finally, after obtaining both of the graphs, we determined that the factor with the largest impact on the distance travelled by the ball, in both designs, was Factor C, the stop length. The factor with the second largest impact was Factor A, the arm length, and the factor with the least impact was Factor B, the ball weight. This was consistent throughout both our tests, and thus, the results are reliable.

After we finished the tasks, we were given a small activity where we were required to compete against other groups in our class to see which group could hit down the most targets. This activity was pretty fun, as the targets had the faces of our lecturers taped onto them, and as such, I was extremely motivated to hit down as many targets as possible. Here's a video of my group performing the activity by destroying Mr Ting.

Overall, I really enjoyed this practical. Not only did we get to apply what we learnt about the full factorial and fractional factorial methods of design, but we also got to apply them in a really fun activity as well, and I look forward to applying what we learnt today in our future prototyping!