Design of Experiment

For the Design of Experiment (DOE) blog entry, I was tasked to perform both full and fractional data analysis for a case study regarding popcorn. Below shows the documentation of my analysis and insights from this case study.

Full Data Analysis

i)

Factor A= diameter

Factor B= microwaving time 

Factor C= power

From the graph shown above, the most significant factor is power of the microwave, followed by the microwaving time then diameter of the bowls.

A: When the diameter of the bowl increases from 10cm to 15cm, the mass of the unpopped popcorn remaining decreases from an average of 1.48g to 1.425g.

B: when the microwaving time increases from 4 minutes to 6 minutes, the mass of the unpopped popcorn remaining decreases from an average of 2g to 0.9g.

C: when the power of the microwave increases from 75% to 100%, the mass of the unpopped popcorn decreases from an average of 2.35g to 0.55g.

The graph shows that the line for the power of the microwave has the steepest gradient followed by the line for the microwaving time and lastly the line for the diameter of the bowl, indicating that the power of the microwave has the biggest impact on the mass of unpopped popcorn remaining, then followed by the microwaving time, and lastly the diameter of the bowl. 

i) For FULL factorial design: (A x B)  

At LOW B, (runs 3 and 8) Average of low A= (0.7 + 3.1)/2 = 1.9 

At LOW B, (runs 1 and 5) Average of high A= (3.5 + 0.7)/2 = 2.1

At LOW B, total effect of A= (2.1 – 1.9) = 0.2 (increase)

At HIGH B, (runs 2 and 7) Average of low A= (1.6 + 0.5)/2 = 1.05

At HIGH B, (runs 4 and 6) Average of high A= (1.2 + 0.3)/2 = 0.75

At HIGH B, total effect of A= (0.75 – 1.05) = -0.30 (decrease)

For FULL factorial design: (A x C)

 

At LOW C, (runs 2 and 8) Average of low A = (1.6 + 3.1)/2 = 2.35

At LOW C, (runs 1 and 4) Average of high A = (1.2 + 3.5)/2 = 2.35

At LOW C, total effect of A = (2.35 – 2.35) = 0 (no effect)

At HIGH C, (runs 3 and 7) Average of low A = (0.5 + 0.7)/2 = 0.6

At HIGH C, (runs 5 and 6) Average of high A = (0.7 + 0.3)/2 = 0.5

At HIGH C, total effect of A = (0.5 – 0.6) = -0.1(decrease)

For FULL factorial design: (B x C)  

At LOW C, (runs 1 and 8) Average of low B = (3.5 + 3.1)/2 = 3.3

At LOW C, (runs 2 and 4) Average of high B = (1.6 + 1.2)/2 = 1.4

At LOW C, total effect of B = (1.4 – 3.3) = -1.9 (decrease)

At HIGH C, (runs 3 and 5) Average of low B = (0.7 +0.7)/2 = 0.7

At HIGH C, (runs 6 and 7) Average of high B = (0.3 + 0.5)/2 = 0.4

At HIGH C, total effect of B = (0.4 – 0.7) = -0.3 (decrease)

Judging from the gradients of the lines in each graph, the strongest interaction is between BxC, followed by AxB then AxC.

The link to the excel file contains the tables and graphs for both full and fractional factorial data used for this assignment: https://drive.google.com/drive/u/0/folders/1aifM4MqxZPmyR6vNxJ5z9UIh1-kJBsl_

In conclusion, the most significant factor is power of the microwave, followed by the microwaving time then diameter of the bowls. The strongest interaction occurs when power of microwave and microwaving time is increased, followed by when diameter of bowl and microwaving time is increased, and finally the weakest interaction occurs when diameter of bowl and power of microwave is increased.

Fractional Data Analysis

i)

Factor A= diameter

Factor B= microwaving time 

Factor C= power

The runs I have chosen to use for the fractional factorial data are 1,6,7,8 as they are orthogonal and balanced.

 

From the graph shown above, the most significant factors are power of the microwave and microwaving time, which are equally significant, followed by the diameter of the bowls.

A: When the diameter of the bowl increases from 10cm to 15cm, the mass of the unpopped popcorn remaining increases from an average of 0.95g to 0.90g.

B: when the microwaving time increases from 4 minutes to 6 minutes, the mass of the unpopped popcorn remaining decreases from an average of 1.65g to 0.2g.

C: when the power of the microwave increases from 75% to 100%, the mass of the unpopped popcorn decreases from an average of 1.65g to 0.2g.

The graph shows that the lines for both the power of the microwave and the microwaving time has equally steep gradients ,followed by the line for the diameter of the bowl which has the least steep gradient, indicating that the power of the microwave and microwaving time has the biggest impact on the mass of unpopped popcorn remaining, followed by the diameter of the bowl. 

The link to the excel file contains the tables and graphs for both full and fractional factorial data used for this assignment: https://drive.google.com/drive/u/0/folders/1aifM4MqxZPmyR6vNxJ5z9UIh1-kJBsl_

In conclusion, the most significant factors in reducing the mass of bullets remaining are both power of the microwave and microwaving time, followed by diameter of the bowl. 

Between full and fractional factorial data analysis, specifically for this case study I would prefer to use the full fractional data analysis as the fractional data analysis did not contain enough data to determine if power of microwave or microwaving time is a more significant factor. Usually, using fractional data analysis nets similar results as full data analysis with less effort needed to compile the data, thus being the more efficient method. However, for this rare case, the data from fractional data analysis is just lacking and more data is needed for this case.