Design of Experiment

Today's lesson, we are tasked to apply the concepts of full factorial design and fractional factorial design on this case study. I decide to go for Case Study 1.

Case Study 1:

This is the scenario for Case Study 1. Right now, I am going to apply what I have learned during the tutorial lesson.

1. Full Factorial Design:

a. Tabulation of Data

After done the data tabulation, I will need to plot the graph using EXCEL to help me to visualize the whole result.

Here is the graph that I have plotted using EXCEL:

b. Effects of Single Factor and their ranking.

Factor A: Diameter of bowls to contain the corn, 10 cm and 15 cm

As the diameter of bowls increases from 10 cm to 15 cm, the mass of the unpopped kernels formed decreases from 1.75 g to 1.5 g.

Factor B: Microwaving time

As the microwaving time increases from 4 minutes to 6 minutes, the mass of the unpopped kernels formed decreases from 2.25 g to 1 g.

Factor C: Power setting of microwave, 75% and 100%

As the power setting of microwave increases from 75% to 100%, the mass of the unpopped kernels formed decreases from 2.50 g to 0.75 g.

c. Interaction Effects among the factors

Interaction Effect (A x B):

At Low B, Average of low A = (0.7+3.1)/2= 1.9

At Low B, Average of high A= (3.5+0.7)/2= 2.1

At Low B, total effect of of A = 2.1 -1.9 =0.2 (increase)

At High B, Average of low A= (1.6+0.5)/2 = 1.05

At High B, Average of high A = (1.2+0.3)/2 = 0.75

At High B, total effect of A = 0.75-1.05 = -0.3 (decrease)

Graph of Interaction Effect on A X B:

From the graph, we can see that the gradient of both lines are different (one is + and other is -). Therefore, there is a significant interaction between A and B.

Interaction Effect (A x C):

At Low C, Average of low A = (3.1+1.6)/2 = 2.35

At Low C, Average of high A = (3.5+1/2)/2 = 2.35

At Low C, total effect of A= (2.35-2.35) = 0 (No change)

At High C, Average of low A= (0.7 +0.5)/2 = 0.6

At High C, 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)

Graph of Interaction Effect on A X C:

From the graph, we can see that there is slightly different in the gradients for both lines. We can conclude that the interaction between A and C are less significant and small.

Interaction Effect (B x C):

At Low C, Average of low B = (3.5+3.1)/2 = 3.3

At Low C, 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, Average of low B= (0.7 +0.7)/2 = 0.7

At High C, 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)

Graph of Interaction Effect on B X C:

From the graph, we can see that the gradient of both lines are negative and different values. Therefore there is a significant interaction between B and C.

Conclusion:

To minimize the mass of the unpopped kernels, we will have to:

1. Use larger diameter of the bowl.

2. Increase the microwaving time.

3. Use high percentage of microwave power setting.

2. Fractional Factorial Design

From the theory that we have learned, I will have to make use of the concept of Statistical Orthogonality.

Here is the guide image on how we can fractionalise:

Since we are doing 8 runs, I will have to separate 4 runs to my other group members, here I proceed to run 1, 2, 3, 6 for the Fractional Factorial Design.

a. Tabulation of Data:

After done the data tabulation, I will need to plot the graph using EXCEL to help me to visualize the whole result.

Here is the graph that I have plotted using EXCEL:

b. Effects of Single Factor and their ranking.

Factor A: Diameter of bowls to contain the corn, 10 cm and 15 cm

As the diameter of bowls increases from 10 cm to 15 cm, the mass of the unpopped kernels formed increases from 0.75 g to 1.0 g.

Factor B: Microwaving time

As the microwaving time increases from 4 minutes to 6 minutes, the mass of the unpopped kernels formed decreases from 1.25 g to 0.5 g.

Factor C: Power setting of microwave, 75% and 100%

As the power setting of microwave increases from 75% to 100%, the mass of the unpopped kernels formed decreases from 1.50 g to 0.25 g.

Conclusion:

To minimize the mass of the unpopped kernels, we will have to:

1. Use larger diameter of the bowl.

2. Increase the microwaving time.

3. Use high percentage of microwave power setting.

Here is the link that you can download and access the excel file:

https://drive.google.com/drive/folders/1veJzJfNklTosSR5uDMpS-aqN3ko8rici?usp=sharing

DOE Tutorial DONE!!!