DOE

Overview 

Hello, welcome back to my blog ! For this week's blog entry, it is about Design Of Experiments (DOE). So what is DOE? DOE is essentially a statistics based approach to designing experiments.

Documentation of case study 

For Case Study 1, I was appointed as the CEO by my group and I was tasked to complete this case study together with my friend, Nikkisha who is the CFO.

Part 1: Determining effect on single factors and their ranking

Recreating the table shown in the PDF, into an Excel file. It looks something like this

Where,

A = Diameter of bowl 

B = Microwaving time

C = Power

However, for ease of convenience. I have replaced the + and - signs to their respective high and low values.

Next, I used this template and filled in the Bullets into the "Average" Column. It is shown as follows

This is the data that I got for filling the values in the above table

With the data that I arrived at, I tabulated the graph and it looks something like this

The ranking most significant to least significant is

1. Factor C
2. Factor B
3. Factor A

Part 2: Full Factorial Data Analysis

The three interaction factors are (A x B), (A x C) and (B x C)

(A x B) 

For this step, I performed Data analysis for full factorial design interaction effect (A x B). I rearranged the values into the table into four sets. The first two row is for Low B, Low A. This is followed by the second set rows three and four, Low B, High A. For rows 5 and 6 they are High B and High A followed by rows 7 and 8, High B Low A. The table looks like this 

Data Analysis:

For Low B

Low B, Avg Low A = (0.7+3.1)/2 = 1.9

Low B, Avg High A = (0.7+3.5)/2 = 2.1

At low B, total effect of A = 2.1 - 1.9 = 0.2 (Increase)

For High B

High B, Avg High A = (1.2+0.3)/2 = 0.75

High B, Avg Low A = (1.6+0.5)/2 = 1.05

At high B, total effect of B = 0.75-1.05 = -0.3 (Decrease)

The graph tabulated is as follows:

Conclusion of Graph: As seen from the graph, the gradient of the two lines are very different. One is positive and the other is negative. This means that there is significant interaction between A and C.

(A x C) 

Similarly for (A x B), I rearranged the graph such that the top quarte is Low C, Low A. The second quarter is Low C, High A followed by the third quarter, High C, Low A  and finally High C, High A. Below is the table that represents the data as mentioned

Data Analysis:

For Low C

Low C, Avg Low A = (3.1+1.6)/2= 2.35

Low C, Avg High A = (1.2+3.5)/2=2.35

Low C, total effect of A = 2.35-2.35= 0

For High C

High C, Avg Low A = (0.7+0.5)/2 = 0.6

High C, Avg High A = (0.7+0.3)/2 = 0.5

High C, total effect of A = (0.5-0.6) = -0.1 (Decrease)

The graph tabulated is as follows:

Conclusion of Graph: As seen, the gradient difference is by a small margin. Hence, there is an interaction between A and C but the interaction is very small

(B x C) 

This section studies the interaction between B and C. Top quarter of the table shows Low C, Low B. Second quarter shows Low C, High B. This is followed by High C, Low B then, High C, High B. Table is as follows

Data Analysis:

For Low C

Low C, Avg Low B = (3.1+3.5)/2= 3.3

Low C, Avg High B = (1.6+1.2)/2= 1.4

Low C, total effect of B = 1.4-3.3= -1.9 (Decrease)

For High C

High C, Avg Low B = (0.7+0.7)/2 = 0.7

High C, Avg High B = (0.5+0.3)/2 = 0.4

High C, total effect of B = 0.4-0.7= -0.3 (Decrease)

The graph is tabulated as follows:

Conclusion of Graph: Both lines have negative gradients and have different values. Therefore, there is a significant interaction between B and C

Part 3: Fractional Data Analysis

For Part 3, the runs selected are

• Run 1
• Run 2
• Run 3
• Run 6
  

This is because all factors occur (both low and high levels) the same number of times. Hence, it is said to be orthogonal and have good statistical properties

Next, I proceeded to narrow down these 4 runs into a table

Data Analysis:

Factor A

Runs where A is + : 3.5 + 0.3 = 3.8/2 = Ave = 1.9

Runs where A is - : 1.6 + 0.7 = 2.3/2 = Ave = 1.15

Total Effect = Difference = 0.75

Factor B

Runs where B is + : 1.6 + 0.3 = 1.9/2 = Ave = 0.95

Runs where B is - : 3.5 + 0.7 = 4.2/2 = Ave = 2.1

Total Effect = Difference = -1.15

Factor C

Run where C is +: (0.7+0.3) / 2 = Ave = 0.5

Run where C is -: (3.5+1.6) / 2 = Ave = 2.55

Total Effect = Difference = -2.05

The graph is tabulated as follows:

Conclusion of Graph:

The ranking most significant to least significant is

1. Factor C
2. Factor B
3. Factor A

This is because C, Power, has the steepest gradient. At a higher power setting, more kernel of popcorn would pop hence, leaving lesser amount of bullets in the bowl. When the power is increased from 75% to 100%, the mass of bullets decreased by 2.05g

For Factor B, microwaving time, it has the second steepest gradient. Hence, it is in the middle of the two factors. The relationship is that the longer the microwaving time, the lower the mass of bullets left in the bowl. This can be seen when the microwaving time is increased from 4 minutes to 6 minutes, the mass of the bullet left in the bowl decreased by 1.15g

Factor A, being the diameter of the bowl, has the least steep gradient. It is thus the least significant factor. The relationship is the larger the diameter of the bowl, the higher mass of bullets left in the bowl. This can be seen when the diameter increases from 10 to 15cm, the mass of bullets increases by 0.75g.