DOE

Hi everyone! Welcome back to my blog! After taking a break, I am back to writing this blog for the documentation of my CPDD lessons. This blog is based on the first topic of this term Design of Experiments. In this blog, I shall show how I solved a case study assigned to me regarding studying the cause of the loss of popcorn yield.

The scenario is as follows:

What could be simpler than making microwave popcorn? Unfortunately, as everyine 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 factoes were identified:

1. Diameter of bowls to contain the corn, 10cm and 15cm
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 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	+	–	–	3.93
2	-	+	–	2.93
3	–	-	+	0.74
4	+	+	-	1.93
5	+	–	+	0.95
6	+	+	+	0.32
7	–	+	+	0.93
8	–	-	-	3.12

Usually, each run is to be done 8 times however I was only given the set of the information shown above. This means that I am unable to calculate the standard deviation and the final result is not as accurate as taking the average for each run over 8 repeats. It should also be noted that although it looks like the values in the table are inaccurate, the values have just been visually rounded up and this does not affect the final result.

Full Factorial analysis:

Put the information into an excel sheet provided

Use the excel sheet to solve for the means of each factor within all runs. This is to find out which factor is more impactful on the final result.

    

Draw a graph in excel that shows the relationship between each factor and the mass of bullets.

Ranking (from most to least significant):

1. Factor C (Power)

2. Factor A (Diameter)

3. Factor B (Microwaving Time)

For Factor C, as the Power increases, the final mass of all bullets decreases the most. It is the most significant due to the difference between its LOW and HIGH points being the largest.

For Factor A, as the Diameter increases, the final mass of all bullets increase. It is the second most significant as it has the second largest difference between its LOW and HIGH points. Although it is a negative effect, it can be shown that by decreasing the diameter of the bowl, the final mass of bullets will also decrease.

For Factor B, as the Microwaving Time increases, the final mass of all bullets also increases by a little bit. It is the least significant due to it having close to no effect on the final outcome at all as it difference between its LOW and HIGH points is incredibly low.

Link to the excel sheet: DOE CPDD Case Study Full Factorial (2).xlsx

Fractional Factorial analysis:

Follow the same steps as before but only use 4 instead

Ranking (from most to least significant):

1. Factor A (Diameter)

2. Factor C (Power)

3. Factor B (Microwaving Time)

For Factor A, as the Diameter increases, the final mass of all bullets increases . It is the most significant due to the difference between its LOW and HIGH points being the largest.

For Factor C, as the Power increases, the final mass of all bullets decreases the most. It is the second most significant as it has the second largest difference between its LOW and HIGH points.

For Factor B, as the Microwaving Time increases, the final mass of all bullets also increases by a little bit. It is the least significant due to it having close to no effect on the final outcome at all as it difference between its LOW and HIGH points is incredibly low.

Link to excel sheet: DOE CPDD Case Study Fractional Factorial.xlsx

This concludes this blog entry! Thank you for reading and hope to see you next time I upload!